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/sci/ - Science & Math

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5738799 No.5738799 [Reply] [Original]

No real values of x can satisfy this equation, yes?
x - x = y
Where y > 0 or y < 0 (meaning non-zero).

And course we could create an imaginary number for this, yes? But here's my question and purpose of this thread..

sqrt(-1) has many applications, does x - x = (non-zero) have any applications any of you could think of?

>> No.5738803

x - x = 0 by definition

error does not compute.

>> No.5738806

No real or imaginary values will satisfy that equation. x-x will always equal zero and will never be non-zero.

>> No.5738845

>hey what if we made an imaginary number that satisfies x^1=/=x
>i'm so funny guys
>haha u got trold
>i'm a trigfag LOLOOL

>> No.5738852

>>5738799
>And course we could create an imaginary number for this, yes?
No, we could not.

>> No.5738876

You're my new favorite tripfag.

>> No.5738888

>>5738799
-+0.0000~001

Only the application of the negative of any number OP

>> No.5738905
File: 5 KB, 259x194, 62362362362.jpg [View same] [iqdb] [saucenao] [google]
5738905

>>5738888
buddhasdick I rolled quad 8's with that

>I'll give offering with the worlds best vagoo

>> No.5738981

I can't think any of those. I can even live without the number i.

>> No.5738983

Neat idea, but no.

x-x /= 0 has no solutions for x, because if it did that would mean that x-x=0=1, a contradiction. As it turns out, imaginary numbers are all you need to find the solutions to any equation that only use powers of x.

>> No.5739005

>>5738905
>worlds best vagoo

Is it soft, warm and slippery?

>> No.5739018
File: 6 KB, 169x251, 1366923917914.jpg [View same] [iqdb] [saucenao] [google]
5739018

>>5739005
and short and tight, that being said male dolphins have a wang with a downwards curv so we'd be missed the gspot; basically the best anal you could give a girl

>inb4 OP's pic of raping dolpins at the aquarium
>Think of the children

>> No.5739022

>>5739018
>short

Since when has short been a good attribute for a vagina?

>> No.5739026

>>5739022
>fucking the back of her throat sucks

>> No.5739028

>>5739026
But you can actually go down the throat, and it also gags her.

Different than ramming your dick against a wall.

>> No.5739198

>>5738799
well that equation simplifies to y=0
Which is is line equation of the x-axis.

>> No.5739210
File: 158 KB, 1229x423, 4chan.png [View same] [iqdb] [saucenao] [google]
5739210

>>5739018

>> No.5739212

>>5738905
This is a worksafe board

>> No.5739911

Everything can be solved by inventing new "imaginary" numbers.

>> No.5740097

>>5739911
No.

>> No.5740138

>>5739210
> that theme

>> No.5740145

>>5739911
For a given value of "solved", which might well happen to be entirely fucking useless.

>> No.5740972

Why don't we just invent an imaginary number that solves x^0=0?

>> No.5740998

Just reading it's clear you're all faggots so let me help quick. Obviously op is the first faggot to pretend imaginary values exist as a solution and are non zero, but that's only because he's a faggot. However, there do exist quotient spaces, for example, where you can find elements satisfying this relation which are non zero. Consider the real affine plane divided by an even integral lattice. This relation there would just stress the toroidal nature of the resultant quotient space. It's not that you're all wrong, you just don't know enough math to think of answers.

>> No.5741019

if we let x=OP then we have
OP-OP=fag, since OP is always a fag

>> No.5741039
File: 25 KB, 465x356, 1322470513671.jpg [View same] [iqdb] [saucenao] [google]
5741039

>>5738799
>trollscience.jpg

>> No.5741046

>>5739911
yeah, fuck group and number theory, IT'S ALL IMAGINARY ANYWAY, RIGHT GAYS?

>> No.5741153

>>5738799
OP! hopefully you haven't been discouraged by other idiots.

your intuition is right, maybe your example is not so much

you might like to look into algebraic varieties and field extensions for interesting stuff and ????? profit

>> No.5742527

>>5741153
What are algebraic varieties and why do we need them?

>> No.5742539

let x be infinity. then you have an indeterminate form, which can be anything.

>> No.5742584

>>5742539

real values only

>> No.5743195

>>5742584
OP's problem cannot be solved in the reals. That's why he needs new imaginary numbers.

>> No.5744030

>>5738803
>by definition

only in the real numbers

>> No.5744097

let x = 1 = (0.999 repeating)

>> No.5744106 [DELETED] 

>>5738799
>And course we could create an imaginary number for this, yes

Nope

>> No.5744117

>>5744030
Hello!

If you were to define an x that satisfied x - x ≠ 0, you would actually be redefining -, because as it stands, writing x - y is by definition x + (-y), where (-y) is the unique element of your [field/group/ring/whatever] that satisfies y + (-y) = 0.

I hope this helps!

>> No.5744135

I don't think OP understands how imaginary numbers work

i - i is still 0

>> No.5744267

OP seriously misunderstands why imaginary numbers exist in the first place.

Let's take a step back and consider the counting numbers and addition. You can add any two counting numbers and wind up with another counting number - this is called "closure under addition".

Now, the counting numbers aren't closed under subtraction (no negative numbers), so let's make up a set of numbers that *is* closed under subtraction. BAM negative numbers.

Closure under division? BAM rational numbers (excluding zero).

Now let's talk about something a bit more complicated. Suppose you have some numbers and a polynomial. You can write that shit two ways:

1. Sum of products (a0 + a1x + a2x^1 ... anx^n).

2. Product of sums k (a0 + x) (a1 + x) (a2 + x)... (an + x)

Now, regular old real numbers are closed under multiplication of polynomials (2->1). But what about the inverse of that (factoring, going 1->2)? Well, you run into issues factoring x^2 + 1, since you need to have a number i such that i^2 = -1 (suppose (x+i)(x-i) = x^2+1). So, we add the imaginary number i to get what is called "algebraic closure".

Now, until you can come up with an explanation at least a tenth as good as that as to why you need a number that makes all sorts of other things ugly (say, that you can find at least one number between any two distinct numbers, and conversely if you can't find at least one number between two other numbers, those two other numbers are the same number), you can just shut the fuck up.

>> No.5744281

>>5744267

i never heard of closure under subtraction before

>> No.5744403

>>5744281
It's nothing fancy, really, it's just a formalization of why you want negative numbers - so that you can perform subtraction and wind up with numbers instead of an undefined operation.

Numbers can be closed under any operation that you can think of, really.

>> No.5744416

>>5744267
For someone with little math background, that was a surprisingly good explanation for things. Thank you

>> No.5745212

First let's make a mathematical formula:
x-x=/=0

Now define x = 1.
1-1=/=0

Replace one of the 1s by 0.999...
1-0.999...=0.00...1=/=0
0.999...-1=-0.00...1=/=0

I hope this helps OP.

>> No.5745238

>>5745212
0.00...1 doesn't exist

>> No.5745259

>>5745238
The limit of (1/10)^n as n approaches infinity does not exist?

>> No.5745261

>>5745238
neither do imaginary numbers

>> No.5745285 [DELETED] 

OP, your question is the reason why they should teach complex numbers in a proper way since high school.

You can't create a new set of numbers out of nowhere and just expect it to work. The right way to think about complex numbers is as an element of the set C = R2, on which addition and multiplication are defined as follows:

(a,b)+(c,d)=(a+c,b+d)
(a,b).(c,d)=(ac-bd,ad+bc)

And then you just consider R to be the subset of (a,b) in C where b=0.

From this you can express every number as (a,b) = (a,0) + (0,b)(0,1) where (0,1)(0,1) = (-1,0) = i.

>> No.5745287

OP, your question is the reason why they should teach complex numbers in a proper way since high school.

You can't create a new set of numbers out of nowhere and just expect it to work. The right way to think about complex numbers is as an element of the set C = R2, on which addition and multiplication are defined as follows:

(a,b)+(c,d)=(a+c,b+d)
(a,b).(c,d)=(ac-bd,ad+bc)

And then you just consider R to be the subset of (a,b) in C where b=0.

From this you can express every number as (a,b) = (a,0) + (b,0)(0,1) (*) where (0,1)(0,1) = (-1,0) = i.

>> No.5745292

>>5745259
It does. It's called 0.

>> No.5745309

>>5745292
Indeed, but it´s a limit, so it`ll never reach it.

>> No.5745423

>>5745259
It does, but it's not 0.00...1

>> No.5747671

>>5745423
Are you retarded? The notation is defined to mean that limit. It's the exact same definition we use when talking about any other kind of repeating decimal.

>> No.5749013

>>5747671
>are you retarded?
putting a number at after ... is not standard in decimal notation. If you want to define <span class="math"> 0.000...1[/spoiler] to be <span class="math">\lim_{n\to\infty} \sum_{k = 1}^{n-1}\frac{0}{10^k} + \frac{1}{10^n} = \lim_{n\to\infty}\frac{1}{10^n}[/spoiler], then <span class="math">0.000...1 = 0[/spoiler] and that's all there is to it.

>> No.5749022

>>5749013
If you have no problem with 0.999... as a different notation for 1, you shouldn't have a problem with 0.000..0001 as a different notation for 0 either

>> No.5749030

>>5749022
As long as you agree that 0.000...01 is 0 with that definition, I'm fine. I simply wouldn't use it because it's incredibly nonstandard and misleading.

>> No.5749034

>>5749030
>because it's incredibly nonstandard and misleading.

Just like 0.999... If you want to say 1, then use the fucking number 1 and not some retarded misleading decimal notation.

>> No.5749041

>>5749034
Well, if I want to write 1, I *would* write 1. However, .999... does not suggest that the decimal terminates after some number of steps, whereas .0...01 suggests that you can have infinitely many decimal places and then somehow stop, which is why I feel that although .999... is a terrible notation for 1, .0...01 is worse (and that's why it's not used at all).

>> No.5749051

>>5749041
>whereas .0...01 suggests that you can have infinitely many decimal places and then somehow stop

whereas 0.999... suggests that the number is smaller than 1

>> No.5749048

>>5749041
>whereas .0...01 suggests that you can have infinitely many decimal places and then somehow stop

Nowhere does it suggest this. If it was finite, we would just write down all the digits. The "..." implies infinity.

>> No.5749063

>>5749051
You wouldn't write down all the digits if it the decimal had 10^(10^10) nonzero digits. And having a "last digit" (the 1 after the ...'s and then no more digits) implies that it somehow does stop or is the last digit, or something which can't actually happen. And sure, if you've never seen the .999... thing before, it seems like .999.... < 1. But as soon as you define it rigorously, there's no problem. The difference is that .99... is a legitimate decimal expansion, while .00...01 is unclear, misleading (in more than one way), and not standard unless there's only a finite number of 0's in the ... bit.

>> No.5749075

>>5745309
But it's still not 0.00..1

>> No.5749076

>>5749075
what's your definition of 0.00...1

>> No.5750138

>>5749076
The definition has been posted ITT

>> No.5750192

>>5738799
Some weird form of modular arithmetic might use it, but otherwise, no dice.

>> No.5750195

>>5750138
0.00...1 is not a Real Number. What set are we working in here? I'd have to know what mathematics you've invented and the formal axiomization before I can comment further.

>> No.5750197

>>5745259
No.
lim n->infinity of (1/10)^n = 0
It doesn't "approach 0". It equals 0.

>> No.5750199

>>5745309
You need to take some basic calc. Do you even know the delta epsilon definition? Ever do a proof with that?

>>5747671
A repeating decimal is generally some computable number, a pattern that can be enumerated by a Turing machine. There is no Turing machine that produces 0.000...0001. It's simply not a Real Number.

>> No.5750202

>>5749034
i^4 = 1 = 2/2 = 1 = 0.999... = 1

>> No.5750204

>>5750199
>There is no Turing machine that produces 0.000...0001.

Are you retarded? Any Turing machine can write "0". Because that's what 0.000....0001 means. It's a different notation for 0, just like 0.999... is a different notation for 1. Or do you disagree that a Turing machine can write "1" because writing infinitely many 9s would never terminate?

>> No.5750206

>>5750199
>Do you even know the delta epsilon definition?

You apparently don't. Your ignorance is cringeworthy. A limit is defined only in terms of epsilon. If you dont' even know the difference between the limit of a sequence and a special case of continuity of a function, I highly doubt you even passed high school calc.

>> No.5750208

>>5750204
0.000...0001 is not a valid decimal expansion.

>>5750206
Talk about pedantics. My point stands. It doesn't "approach 0". It equals 0. And yes I'm familiar with the different definitions of limits of sequences and for Real to Real functions.

>> No.5750212

>>5750208
>0.000...0001 is not a valid decimal expansion.
It has been defined as a limit. Just like 0.999... Did you not even read the thread before posting? You're embarrassing yourself.

>> No.5750215

>>5750208
>And yes I'm familiar with the different definitions of limits

Apparently you're not. If you were, you wouldn't confuse them on such a fundamental level.

>> No.5750218

>>5750212
You can't define it as a limit.

0.999... has a common definition, namely of:
lim n->infinity of sum i=0 to n of f(x) * (1/10)^i
where f : R -> R, and for all x in R, f(x) = 9

You cannot do a similar construction for 0.00...001.

>> No.5750219

>>5750218
>You can't define it as a limit.

I can and I did. See >>5745259. Are you trolling or mentally impaired?

>> No.5750220

>>5750218
(Ack, might have an off by one error. This is me not caring though.)

>> No.5750223

>>5749013
>>5745309
>>5745292
>>5750197

The correct answer is that the limit is 0, and the number 0.000....1 resolves to 0 also.

This is pretty plain when you look at an iterative form of the question.

Start with the number 1, and divide by 10 for each iteration. Th out put after n iterations is equal to (1/10)^n

As we progress the iterations, the number out put gets smaller, as expected.

So by a logical extension, an infinite number of iterations would produce a number that is infinitely small, which by definition is equal to 0.

Because that's what 0 represents, the lack of anything.

>> No.5750224

>>5750219
That's 0.000...
Not 0.000...0001
The second is simply ill-defined. The notation is bullshit. No one uses it. You can't find a single legitimate math textbook or paper that uses that notation, except to make fun of it. There is no formalization that allows for something after an infinite pattern to be meaningful. It's like saying
0.000...000pie is identified as the limit which equals 0.

I, and the rest of academia, reject out of your hand your stupid bullshit notation that says
0.000...0001
is the same thing as
0.000...

>> No.5750230

>>5750218
Yes you can pull a similar construction because 0.0000....1 is equal to zero in definition, see
>>5750223

>> No.5750234

>>5750224
>That's 0.000...
>Not 0.000...0001
That's the same number, you fucking retard. Numbers can have more than one representation, as evidenced by 1 and 0.99...

>The second is simply ill-defined.
I defined the notation ITT. The limit is well defined. Your childish appeal to emotion does not invalidate calculus.

Holy shit, I seriously hope you're trolling.

>> No.5750236

>>5750230
It's not equal to anything. It's not a legitimate decimal expansion.

A decimal expansion is a sequence, a function from the Naturals to {0,1,2,...,8,9}. There is no such function that can be identified with
0.000...0001
It's bullshit.

>> No.5750239
File: 12 KB, 300x100, they sure are mad.png [View same] [iqdb] [saucenao] [google]
5750239

>>5750224
Pic related.

This is /sci/. If you somehow can't convince the other party to be rational, their loss.

>> No.5750247

>>5750236
You idiot, the dots are placeholders for the infinite number of zeroes that would take an eternity to write out. It's an informal goddamn shorthand, for a number that happens to satisfy the parameters you describe.

>> No.5750251

>>5750247
What does that have to do with my point? There is no function f : N -> {0,1,2,...,8,9} which can be identified with 0.00...001
There is a function f : N -> {0,1,2,...8,9} which can be identified with 0.999...

This is two questions, a question about shorthand and notation, and a question about what is a legitimate decimal expansion.

>> No.5750252

>>5750236
The notation has been defined ITT and it was shown to be meaningful and consistent. From someone who claims to have a BSc in math I would expect to understand a simple notation that can be defined within one line. Would you mind telling me some of the "higher" math classes you took?

>> No.5750256

>>5750252
I fail to see a coherent definition that is consistent with basic Real Analysis and the usual conventions and definitions of the mathematics community.

>> No.5750259

>>5750251
Did you react equally childish in your math classes when new notations were introduced? I can imagine you sittinng there and saying "bawwww, noooooo!! I don't like the way singular homology is defined, therefore it makes no sense and is no math!!! cry cry cry"

>> No.5750264

>>5750256
Are you seriously saying that the limit of (1/10)^n as n approaches infinity does not exist? Seriously? This is below shit tier trolling.

>> No.5750267

>>5750259
This is not a matter of introducing new notation. This is indicative of a fundamental misunderstanding of the issues involved.
0.999... is well defined because there exists an obvious associated decimal expansion. 0.000...0001 does not have an obvious associated decimal expansion. It is not a decimal expansion.

>>5750264
>Are you seriously saying that the limit of (1/10)^n as n approaches infinity does not exist? Seriously? This is below shit tier trolling.
That limit does exist. The limit is also 0. Entirely separate question.

>> No.5750268

>>5750251
why and how does this
>>5745259
function not meet those parameters.

>> No.5750271

>>5750268
How is that a function f : N -> {0,1,2,...,8,9} ?

>> No.5750272

>>5750264
Notation issues notwithstanding, the limit is or is equivalent to 0.

See my explanation here >>5750223

>> No.5750275

>>5750267
>This is not a matter of introducing new notation.
It is a notation and it is well-defined and consistent. Math is based on logic and not on your irrational emotions. Decimals are a notation. What else do you think they are? Religious dogma? Way to show your lack of mathematical education.

>> No.5750276

>>5750267
>That limit does exist. The limit is also 0. Entirely separate question.

The question isn't separate. If you agree the limit exists, then the notation defined ITT is well-defined.

>> No.5750277

>>5750271
because 0.000....1 as defined by the function that produces, matches the definition of 0

>> No.5750278

>>5750275
Again, take it from someone who knows more than you do.

0.000...0001 is not a decimal expansion. There is no decimal expansion that is identified with the insane shorthand of "0.000...0001". A decimal expansion is a function f : N -> {0,1,2,...,8,9}

>>5750277
I don't care. If you cannot define the associated decimal expansion function f : N -> {0,1,2,...,8,9}, then you do not have a decimal expansion. Instead, you have gibberish.

>> No.5750279

>>5750275
>>5750276
...
>>5750272

>> No.5750280

>>5750271
How is this relevant? Why are you incapable of understanding how the notation has been defined ITT? Have you never read a math book? Authors constantly define new notations. Please finish high school and don't talk about things you don't understand.

>> No.5750282

>>5750280
Because that's the well accepted definition of a decimal expansion. You do not get to invent a new notation and number system and reuse old words that refer to inconsistent concepts. 0.000...0001 is meaningless gibberish. It is not a decimal expansion.

>> No.5750283

>>5750278
>someone who knows more than you do.
You do not know more than me. You don't even know babby math, you fucking high school troll. Obvious 0/10.

>is not a decimal expansion
It has been defined ITT. Do you not understan the definition?

>> No.5750285

>>5750278
>I don't care

In other words you are dismissing a valid mathematical definition for childish emotional reasons. Please get the fuck out of the math board.

>> No.5750286

>>5750278
dude, who gives a bitch about decimal expansions, it's a valid decimal string that exists on the real line, and hence can so totally be a limit of some function f E R

>> No.5750287

>>5750286
I don't know what a "decimal string" means. It's not defined in any math textbooks or papers which I've read. If you're going to invent terms, please properly define them. What is a "decimal string"?

>> No.5750288

>>5750282
The notation has been defined and was shown to be meaningful and consistent. Do you also cry every time an author introduces a new notation in a math book? Oh wait, you never read one.

>> No.5750289

>>5750288
If an author was stupid enough to introduce a new notation with the same name as an existing convention in an inconsistent way, yes I would bitch, as would everyone else.
0.000...0001 is not a decimal expansion.

>> No.5750290

>>5750287
>I don't know what a "decimal string" mean

Seriously? Lurk the fuck more. Take a math class. Read a book. Just stop posting.

>> No.5750291

>>5750289
The notation has been defined. What is your fucking problem? Stop polluting this thread with your insane and irrational trolling garbage.

>> No.5750292

>>5750290
As what happened in the other thread, I am more than willing to provide sources, citations, and links to online textbooks, papers, and such. For example, I did so for the definition of "decimal expansion". Are you? Could you please define what you mean by "decimal string"? Do you simply mean a collection of characters in a certain order? Then yes, it's a string. Congrats.

>> No.5750293

>>5750291
Your "definition" is inconsistent with the usual conventions. That makes your notation stupid.

>> No.5750294

>>5750287
decimal string; string of natural numbers which includes a decimal point, that defines some n E R.
A term more related to coding, but more or less accurate in description.

0.0000...1 is a valid decimal value, that exists within the set of real numbers R, and hence is a valid limit for some function f E R.

That is the point I wish to get across. I can provide proof if need be.

>> No.5750298

>>5750292
I am not here to give you a lecture after you ruined this thread with asinine shitposting, insults and trolling. You came here spouting ignorance of the worst kind. You claimed to have a BSc in math, yet you fail to understand simple definitions. I'll give you a 1/10 for your obstinacy.

>> No.5750299

>>5750293
The notation is consistent and useful and extends the very limited expressiveness of your outdated elementary school definition. Do you not into math?

>> No.5750302

>>5750294
>decimal string; string of natural numbers which includes a decimal point, that defines some n E R.
Defines how? What's the exact process for going from a "decimal string" to a Real? I think you'll find that you will implicitly define a function f : N -> {0,1,2,...,8,9}, and you will also find that there is no function f : N -> {0,1,2,...,8,9} which describes 0.000...0001.

>0.0000...1 is a valid decimal value, that exists within the set of real numbers R, and hence is a valid limit for some function f E R.
What do you mean "decimal value"? It's not a decimal expansion. Could you define what you mean please?

>> No.5750303

>>5750299
Perhaps it's internally consistent and "useful", but it is not a decimal expansion, and the definition you propose is non-obvious. I'm still waiting for a formal definition.

>> No.5750306

>>5750303
>non-obvious

Math stops being valid when it isn't "obvious" anymore? That sounds like something an anti-intellectual high schooler would say. Have fun failing your "abstract" math clases (if you ever get to take one).

>> No.5750307

>>5750306
For your knowledge, Math 525 Abstract Algebra was one of the hardest courses I've ever taken. Happened to have it taught by a prof who specialized in the area. Was the only undergrad in the class. 3/4 of the class dropped out before the end. Possibly the only course that I didn't get intuitively and had to work my ass off for.

>> No.5750309

>>5750306
And yes, if it is non-obvious in math, then you need to provide a formal definition. I'm still waiting for that.

A string "0.999..." has a straightforward conversion to a formal decimal expansion f : N -> {0,1,2,...,8,9}. That is the formal definition of a decimal expansion used in every textbook and paper.

There is no textbook or paper which describes how to convert "0.000...0001" to a decimal expansion. That's why I'm asking you to do so, or admit that it's not a decimal expansion.

>> No.5750310
File: 19 KB, 350x272, hahahaohwow.jpg [View same] [iqdb] [saucenao] [google]
5750310

>>5750307
>Abstract Algebra was one of the hardest courses I've ever taken

>> No.5750313

>>5750302
OK, so I made assumptions over your notation.

you want a function of f such that the set of natural numbers N are contained within the set [0,1,2,3,4,5,6,7,8,9]?
Because that, to me, IS a load of gibberish.

I assume you mean that you want a function f whose output*(10)^n may be mapped to the set [0...9], where n E N.

In which case, let n=infinity, as infinity is actually included within the set of natural numbers N. The function then maps to the number 1, which is in the set.

Ta-da.

>> No.5750314

>>5750310
I take it you haven't taken that many college level math courses.

>> No.5750315

>>5750307
Abstract algebra is among the first undergrad freshman courses. How fucking hard are you failing?

>> No.5750317

>>5750313
>you want a function of f such that the set of natural numbers N are contained within the set [0,1,2,3,4,5,6,7,8,9]?
>Because that, to me, IS a load of gibberish.
That's clearly what I have been writing, many many times. Please pay attention.

That is the formal definition used in every textbook and paper.

>>5750315
Take some more math courses, or do some research, and stop speaking out of your ass.

>> No.5750318

>>5750314
Would you mind answering me a few questions on sheaf cohomology, you omniscient math god?

>> No.5750319

>>5750318
>you omniscient math god?
Please. I never said that. However, I am quite well versed enough for this inane conversation.

>> No.5750321

>>5750317
>Take some more math courses

Which ones do you want me to take?

>> No.5750324

>>5750319
>failed algebra
>claims to be a mathematician

top lel

>> No.5750325

>>5750321
Enough to realize that there may be several courses that may be named "abstract algebra", and some of them will kick your ass if you're just an undergrad.

Real Analysis is a good start too. Understand the Cauchy construction and Dedekind construction of the Reals. If you did, you should understand why "0.000...0001" is gibberish.

>> No.5750327

>>5750317
Let me ask again. Some function, f, such that:

The ENTIRE NATURAL LINE, N, IS A SUBSET OF THE SET [0,1,2,3,4,5,6,7,8,9]

THIS, is what you want in particular?

>> No.5750330

>>5750325
>that there may be several courses that may be named "abstract algebra"
Tell me about the contents. What did you learn?

>Real Analysis is a good start too
Real analysis is the first course in the first semester at university. From someone who claims to have a BSc I would expect some more profound knowledge.

>why "0.000...0001" is gibberish.
A definition of this notation has been posted ITT.

>> No.5750334

>>5750327
Are you familiar with the notation f : A -> B?
This means that f is a function that maps all values in A to values in B.

For example, f : N -> N, f(x) = x
For example, f : R -> R, f(x) = x
For example, f : N -> R, f(x) = x
For example, f : R -> N, f(x) = | floor(x) | + 1

A decimal expansion is a sequence of digits, aka a function f : N -> {0,1,2,3,4,5,6,7,8,9}.

0.999... is a common well understand shorthand notation that refers to the decimal expansion f : N -> {0,1,2,3,4,5,6,7,8,9}, f(x) = 9

0.2 is a common well understand notation that refers to the decimal expansion f : N -> {0,1,2,3,4,5,6,7,8,9},
f(x) =
2, x = 1
0, x > 1

I'm asking for you to provide that for the string 0.000...0001
You cannot, because there is no finite Natural n that corresponds to the decimal place of the "1" digit. That's why it's not a decimal expansion, and that's why you will never see that notation in any textbook or paper.

>> No.5750340

>>5750330
>Real analysis is the first course in the first semester at university. From someone who claims to have a BSc I would expect some more profound knowledge.
Not in the US it's not. I doubt even in the better European countries it's like that either. At least in the US, you generally do multivariable calc before you take Real Analysis IIRC, making it more like second term or later even for those US students who did the calc BC AP test in high school and got the credit accepted at university.

>> No.5750343

>>5750334
I hope you do realize that by your fucked up pseudo-intellectual high schooler fail definition 0.999... and 1 are not equal. The map f: N --> {0, ..., 9} representing 0.999... is different from the map representing 1. Therefore your definition is inconsistent with the definition of the reals and therefore utter crap.

>> No.5750344

>>5750334
In any case, I don't care. I looked at the core concept the invalid notation wished to express; it wished to express the values 0.0000, for all practical intents and purposes. See here
>>5750223
for an explanation of why and how this is so.

Notation be damned, the question is a valid question to ask, and I have given a correct and comprehensible answer.

>> No.5750346

>>5750340
>Not in the US it's not.
Tell me about the US. What's the highest math you have to take before getting a Bachelor's degree. From your ignorant posts ITT I have to assume they are handing out degrees for anyone.

>I doubt even in the better European countries it's like that either
You are wrong.

>> No.5750348

>>5750343
I hope you understand that it's nonsensical to refer to the equality of a Natural number and a real-valued sequence without a lot of underlying infrastructure that you would know if you had taken some basic Real Analysis.

Using the Cauchy construction of the Reals, it is trivial to construct the Cauchy series of the decimal expansion f : N -> {0,1,2,3,4,5,6,7,8,9}, f(x) = 9, and under the usual rules of equality for Reals under the Cauchy construction, to show that the Cauchy series equals the Cauchy series 1 = 1 + 0 + 0 + 0 ... .

>> No.5750351

>>5750348
>real-valued sequence
Probably should be rational-valued in context. My bad.

>> No.5750352

>>5750348
Using Cauchy sequences it is also trivial to show that the notation 0.00...001 defined ITT happens to be a valid representation of the number 0.

>> No.5750355

>>5750352
There is no Cauchy sequence identifiable with 0.00...001. That's the problem.

>> No.5750358

>>5750355
It's like you're actually reading impaired. (1/10)^n is a Cauchy sequence.

>> No.5750364

>>5750361
Look at the definition that has been posted ITT. The notation is DEFINED by that Cauchy sequence.

>> No.5750361

>>5750358
Correct. And unrelated. 0.00..001 has no associated Cauchy sequence.

>> No.5750366

I wish stupidity was bannable. This retarded tripfag ITT Is giving me cancer.

>> No.5750370

>>5750355
In any case;
>>5750223

I've used an iterative version of the function that brought this whole debate up to show that the limit is 0, and that the conceptual decimal expansion 0.000...1 would resolve to zero were that decimal expansion valid.

>> No.5750371

>>5750358
Here. Let me try and spell this out for you.

Let's take 1/3
This has the decimal expansion
0.333
aka
f(1) = 3
f(2) = 3
f(3) = 3
etc

The associated Cauchy sequence under the Cauchy construction of the Reals is
f(n) = 3 * (1/10)^n

The Cauchy series is
lim n->inf of sum i=1 to n of 3 * (1/10)*n

Now,
f(n) = (1/10)^n is a Cauchy sequence.
The Cauchy series is
lim n->inf of sum i=1 to n of (1/10)^n
This has the decimal expansion
0.111...
aka f(1) = 1, f(2) = 1, f(3) = 1, ...
This is equal to the rational 1/9.

Please try to read that for comprehension.

>> No.5750373

Ack. Fixed:

Here. Let me try and spell this out for you.

Let's take 1/3
This has the decimal expansion
0.333...
aka
f(1) = 3
f(2) = 3
f(3) = 3
etc

The associated Cauchy sequence under the Cauchy construction of the Reals is
f(n) = 3 * (1/10)^n

The Cauchy series is
lim n->inf of sum i=1 to n of 3 * (1/10)*n

Now,
f(n) = (1/10)^n is a Cauchy sequence.
The Cauchy series is
lim n->inf of sum i=1 to n of (1/10)^n
This has the decimal expansion
0.111...
aka f(1) = 1, f(2) = 1, f(3) = 1, ...
This is equal to the rational 1/9.

Please try to read that for comprehension.

>> No.5750377

>>5750371
>>5750373
Why are you intentionally misintepreting my posts? Why do you enjoy trolling this board so much?

>> No.5750378

>>5750373
Shorter:
The decimal expansion
0.111...
has the associated Cauchy sequence
f(n) = (1/10)^n
has the associated Cauchy series
lim n->inf of sum i=1 to n of (1/10)^n
which equals the rational 1/9

The decimal expansion
0.00...0001
does not have an associated Cauchy sequence under the Cauchy construction of the Reals.

>> No.5750383

>>5750373
Not every Cauchy sequence resuls in a convergent series. You failed at real analysis.

>> No.5750381

>>5750377
I'm not misinterpreting anything. You're the one who can't keep up. It's not my fault. I'm trying to explain this as best I can.

>> No.5750386

>>5750378
Are you a scientist irl?

>> No.5750392

>>5750390
Ooh, my bad. Confused sequence and series there. My bad. Yes.

>> No.5750390

>>5750383
>Not every Cauchy sequence resuls in a convergent series. You failed at real analysis.
What?
http://en.wikipedia.org/wiki/Cauchy_sequence

That's how the word "convergence" is commonly goddamned defined in textbooks, in terms of Cauchy sequences.

>> No.5750391

>>5750386
Of course he isn't. He's a failed high school troll who doesn't evn understand the basics of math.

>> No.5750389

>>5750381
You refuse to understand a simple consistent definition. Your anti-intellectualism is sickening.

>> No.5750393

>>5750364

In any case, an attempt at using the Cauchy sequence to construct the decimal expansion 0.000...01 won't work; you won't ever reach the last zero, by definition, and you just end up with a stupid long string of 0's

>> No.5750394

>>5750390
http://en.wikipedia.org/wiki/Sequence
http://en.wikipedia.org/wiki/Series_%28mathematics%29

Are you not even embarrassed of your stupidity?

>> No.5750395

>>5750390
>Hurr durr every space is banach

>>5750391
I figured as much.

>> No.5750397

>>5750383
You are right. Every converging series of Rationals identifies a Real. There is a common notation and convention that maps a decimal string to such a Cauchy series of Rationals. The common mapping does not have a defined result for 0.000...0001 because it is not a decimal expansion.

>> No.5750400

>>5750392
quite possibly, yeah.

>> No.5750401

>>5750395
Read the thread. It's hilarious. He struggled with babby's first abstract algebra and he thinks freshman real analysis is the hardest math course of all times.

>> No.5750403

>>5750401
You're the one showing your ignorance if you think that freshmen "abstract algebra" is the same thing as grad level Math 525.

>> No.5750404

>>5750397
>>5750395
>>5750394
>>5750392
>>5750391
>>5750390
>>5750389
>>5750386
>>5750383
>>5750381
>>5750378
>>5750373
ALL OF YOU

>>5750393

>> No.5750406

>>5750397
What part of the definition posted ITT do you not understand?

>> No.5750408

>>5750406
The part where 0.00...001 can be mapped to a Cauchy series of Rationals under the usual Cauchy construction of the Reals.

>> No.5750409

>>5750403
Tell me what you learned in that course.

>> No.5750410

>>5750408
Are you saying that 0 is not a real number?

>> No.5750411

>>5750390
0/10

>> No.5750413

>>5750390
Plain wrong.

>> No.5750412

>>5750410
No. 0 is a Real. The Cauchy series
lim n->inf of sum i=1 to n of 0
is a Cauchy series of Rationals that is by convention equal to the Rational 0. We refer to that Cauchy series as the Real 0, which by convention equals the Rational 0.

0.00...001 is not a decimal expansion.

>> No.5750416

>>5750412
The notation has been defined as the limit of a convergent sequence. Where is your problem? What do you not understand?

>> No.5750415

>>5750413
I like how everyone misses where I corrected myself immediately afterwards. Oh well.

>> No.5750418

>>5750416
I agree that lim n->inf of (1/10)^n = 0.
I agree that that is a Cauchy sequence of Rationals identifiable with the Real 0.

That doesn't make 0.00...001 a decimal expansion, or not gibberish.

>> No.5750421

>>5750418
Well then why not look at any number of the posts in this thread who have taken this gibberish and extracted from it the writers intent?

>>5750344

There you go. Crisis solved.

>> No.5750422

>>5750412
Simple question for you:

If I wrote "x=0", would you start crying and flailing your arms around while throwing a tantrum "noooo, x cannot be a real number. x is a letter and letters are not series of natural numbers"? Because that's exactly what you're doing ITT. Someone defined a different notation for something which evaluates to 0. In math this is a normal procedure.

>> No.5750423

>>5750418
Again, a decimal expansion is a function f : N -> {0,1,2,3,4,5,6,7,8,9}

The Real number of a decimal expansion is the Cauchy sequence:
f(n) = sum i=1 to n of decimal_expansion(i) * (1/10)^i
That's the definition of decimal expansion in every textbook and paper.

>> No.5750424

>>5750422
I don't know what your problem is. All I've been saying is that 0.00...001 is not a decimal expansion. This is quite straightforward to anyone who knows anything on the subject.

>> No.5750428

>>5750418
It is a notation and it has been defined rigorously. Where is your problem?

>> No.5750431

>>5750424
And all the rest of us are asking is, WHY DO YOU CARE? The rest of us gleaned what he meant 50 posts back, and have already given him the answer.

>> No.5750430

>>5750428
I'm still waiting for the rigorous definition ala:
>>5750423
>Again, a decimal expansion is a function f : N -> {0,1,2,3,4,5,6,7,8,9}
>The Real number of a decimal expansion is the Cauchy sequence:
>f(n) = sum i=1 to n of decimal_expansion(i) * (1/10)^i
>That's the definition of decimal expansion in every textbook and paper.

>> No.5750432

>>5750424
How retarded are you? Nobody is talking about "decimal expansions" the way YOU defined them. We have presented a consistent and meaningful mathematical notation ITT. Despite its mathematical rigor you dislike it for emotional reasons and mindlessly attack it on the formally incorrect basis of inappropriately confusing it with your flawed definition.

>> No.5750433
File: 14 KB, 300x330, duty_calls.png [View same] [iqdb] [saucenao] [google]
5750433

>>5750431
Because duty calls. Someone posted something which IMHO can very easily lead to a gross misunderstanding of basic calc.
0.999... is well defined because it is a commonly used shorthand notation that is trivially mappable to a decimal expansion.
0.00...001 is a bullshit notation because no one uses it, and it has no mapping to a decimal expansion.

>> No.5750435

>>5750432
What mathematical rigor? I've been asking for that for a while. What is the process by which you convert a decimal string like "0.00...001" to a Cauchy sequence of Rationals? Because that's the only way to make it a Real.

>> No.5750436

>>5750424
>is not a decimal expansion

So fucking what? Nobody claimed it was and it is still defined consistently. "Hurr durr an apple is not a banana." Is this your argument? You are severely mentally deficient.

>> No.5750439

>>5750435
I'm asking for a formal definition like:

>>5750423
>Again, a decimal expansion is a function f : N -> {0,1,2,3,4,5,6,7,8,9}
>The Real number of a decimal expansion is the Cauchy sequence:
>f(n) = sum i=1 to n of decimal_expansion(i) * (1/10)^i
>That's the definition of decimal expansion in every textbook and paper.

>> No.5750441

>>5750436
Then I fail to see what the problem is, because all I've been saying is that it is not a decimal expansion, and it's a notation that is not used by any textbook or paper, and it should not be used because it is indicative and can lead to a gross misunderstanding of the usual Cauchy construction of the Reals. And will make you look like an idiot if you use it with math people who know what they're doing.

>> No.5750445

>>5750433
>it is a commonly used shorthand

Fucking nobody is using 0.999... instead of 1 in any context other than demonstrating the obscure fact that these decimal expansions happen to represent the same number.

>> No.5750450

>>5750445
Here are some textbooks and course outlines which do:

Math 101: Course Summary
Rich Schwartz
August 22, 2009
http://www.math.brown.edu/~res/DUS/Summary/M101Summary.pdf
>What is a Real Number? Most people have known about real numbers since grade school. A rough and ready way to describe a real number is that anything with a decimal expansion is a real number. Numbers like 17 and PI = 3.1415926... are examples of real numbers. With this definition, you have to be a bit careful. The two expressions .99999... and 1 both describe the same number. So, you would really have to say that a real number is a decimal expansion, but with the proviso that certain decimal expansions name the same number. To be formal about it, you could say that the decimal expansion 3.14159... is the limit of the series
> 3 + (1/10) + (4/100) + (1/1000) + (5/10000) + (9/100000) + ... .
>So, first of all, you would have to know about about series and limits. Then, you would have to say that a real number is really an equivalence class of such expansions. Making the decimal expansion definition work is actually a bit clumsy, and so a real analysis class usually takes different (but closely related) approaches.

http://www.math.utah.edu/~bertram/courses/4030/Reals.pdf
> Examples: (a) The natural number m expands as the terminating decimal:
> m.000000 · · ·
> The infinite decimal:
> (m - 1).99999 · · ·
> also represents m,

>> No.5750451

>>5750430
why does the rigorous definition have to fit the definition for a decimal expansion when we already know that it is not this.

A rigorous construction;
take the number 0
add an infinite amount of 0's on.
add a one to the beginning,
reverse the entire number so the one now sits on the other side of the infinite number of 0's
add a decimal dot after the first 0

And now a rigorous definition;

Take the number 1.
Divide it by 10
repeat steps 1 and two an infinite number of times.

>> No.5750452

>>5750439
>I'm asking for a formal definition

It has been posted so many times ITT:
0.00...001 equals the limit of (1/10)^n as n approaches infinity.

>> No.5750453

>>5750450

http://homepage.cs.uiowa.edu/~fleck/ratnote.pdf
>Assertion: Each rational number has a periodic decimal expansion, and every number with a periodic decimal expansion is a rational number.
0.9... (repeating) is a periodic decimal expansion, and thus it is a rational number, and thus (obviously) it is 1.

http://www.math.ubc.ca/~cass/courses/m446-05b/dedekind.pdf
> 1. Inadequacy of infinite decimal expansions
> In practical terms, one would be tempted to identify a real number with its decimal expansion. Of course this can’t be quite valid, since some numbers have two decimal expansions:
> 1.00000000... = 0.9999999999...

http://www.springer.com/cda/content/document/cda_downloaddocument/9780387980973-c1.pdf?SGWID=0-0-45-813443-p173916008
[Slightly modified for formatting]
> One difficulty with using infinite decimal expansions to define the real num-bers is that some points have two names. For example consider the expansions
> 1.000000000... and 0.999999999...
> Call them 1 and z, respectively. Clearly these are different infinite decimal expansions. However, for each positive integer k,
> 1-10^-k = 0.9999999999999...9 [number of '9's = k] <= z <= 1.
> Thus the difference between z and 1 is arbitrarily small. It would create quite an un-intuitive line if we decided to make z and 1 different real numbers. To fit in with our intuition, we must agree that z=1. That means that some real numbers (precisely all those numbers with a finite decimal expansion) have two different expansions, one ending in an infinite string of zeros, and the other ending with an infinite string of nines. For example, 0.12500... and 0.12499999... are the same number.

>> No.5750454

>>5750441
> can lead to a gross misunderstanding

Stop projecting. The only one misunderstanding real analysis ITT is you.

>> No.5750455

>>5750451
That's not a formal process. It never terminates. A formal process must terminate in finite time.

>>5750452
I don't know what "0.00...001 equals the limit" means, because 0.00...001 does not name a Real Number as far as I know, because it's not a proper decimal expansion. Are you defining the string "0.00...001" specially? What general process do you have to convert that string to a Cauchy sequence of Rationals?

>> No.5750457

>>5750453
So, you see, textbooks frequently use that as an example. You will not find a textbook that uses the notation "0.00...001" except to note that it is malformed.

>> No.5750459

I'm new to /sci/. Is the "Scientist" tripfag your resident village idiot? His posts are cringeworthy.

>> No.5750461

>>5750459
I'm possibly the oldest tripfag on /sci/. I'm sorry for being pedantic anal. If they have no problem with my claims, then they shouldn't post as though they were disputing them. It's not a decimal expansion. It's a notation that would be marked off in any college class as informal and ill-defined.

>> No.5750462

>>5750455
>I don't know what "0.00...001 equals the limit" means,

It is a fucking definition.

[term to be defined] = [expression]

>> No.5750463

>>5750455
He doesn't need a general process, because he's defining for a specific case, which he can, because the definition for this specific case was implied in the original question.

>> No.5750468

>>5750455
> because 0.00...001 does not name a Real Number

IT HAS BEEN DEFINED AS THE REAL NUMBER 0, I.E. THE LIMIT OF (1/10)^N AS N APPROACHES INFINITY. WHAT THE FUCK DO YOU NOT UNDERSTAND?

>> No.5750471

>>5750455
why does it have to be a formal process? Plenty of irrationals are defined as infinite series, and those won't terminate either.

>> No.5750472

>>5750461
You are not pedantic, you are simply illiterate. Nobody is talking about "decimal expansions". We are assigning a value to a symbolic string.

>> No.5750469

>>5750462
So, you're defining the string literal "0.00...001" to be equal to the Real 0? Ok. What about the string literal "0.000...0001"? Do you really want to do this? I would mark your answer as wrong in any math class that I taught.

>> No.5750474

>>5750472
See:
>>5750469
>So, you're defining the string literal "0.00...001" to be equal to the Real 0? Ok. What about the string literal "0.000...0001"? Do you really want to do this? I would mark your answer as wrong in any math class that I taught.

>> No.5750476

>>5750469
You will never teach a math class because you are already failing high school math. I wouldn't ever want a teacher you doesn't even understand what a definition is.

>> No.5750479

>>5750469
nononononononono

He is defining the conceptual and unwriteable string that is 0.0 with an infinite number of 0's after it and then a 1 as a representation of the number 0.


I thought that bit was implicit.

>> No.5750480

>>5750469
>What about the string literal "0.000...0001"?

That's the same string. A countably infinite number of zeros is still a countably infinite number of zeros.

>> No.5750483

>>5750476
I'm sorry that I'm being a bad teacher right now. I don't know how else to explain it. The notation is not a decimal expansion. The notation is not in use by any textbook or paper. The notation is problematic precisely because it tries to put a "1" after an endless amount of zeroes, which goes against all of basic calc. It's malformed gibberish. You should not use that notation.

>> No.5750489

>>5750480
no it isn't, because thats not what string literal means. String literal is 'what you see inside the double quotes is what you get'.

You, and everyone else inna thread, mean this>>5750479

>> No.5750487

>>5750479
Ok. What about the string literals of the form "0.000...0002"? Would he define that as 0? Should I expected to see this as obvious? It's not.

>> No.5750491

>>5750480
That's not the same string literal. The string
"0.00...001"
Has 5 '0' characters, 4 '.' characters, and 1 '1' character.

I'm asking for you to tell me the process or algorithm by which I can judge which string literals you provide are equal to one another.

>> No.5750492

>>5750483
> I don't know how else to explain it.
I have been explaining several time why you are wrong and retarded. You didn't even understand the problem.

>The notation is not a decimal expansion.
Nobody claimed it was. We are NOT talking about decimal expansions.

>It's malformed gibberish.
It has been defined rigorously and consistently.

>> No.5750493

>>5750489
>>5750491
>can't into infinite strings

>> No.5750497

>>5750492
Is the string literal "0.000...0002" equal to 0?
Is the string literal "0.000...000222...222..." equal to 0?

>>5750493
Sorry, I don't read minds. I'm asking you to explain yourself.

>> No.5750502

>>5750497
Anything times zero is zero.

>> No.5750505

>>5750497
If you prefer, you could write some C or C++ or some Java code which decides (in finite time) if the given String literal equals 0. That might make this easier.

>> No.5750512

>>5750505
Math doesn't care about plebian code monkey work.

>> No.5750513

>>5750508
Obviously. I'm trying to entice that answer out of him. Hopefully in doing so he'd realize how retarded that shit is.

>> No.5750508

>>5750487
Go back and examine the question he is trying to ask. It may be non obvious, but from the core concept he is trying to express I have gleaned the following rule:

So long your string can be represented in the form 0.000nx
where n is representative of an infinite number of 0's concatenated to the string, and x is any natural number also concatenated,

your string will represent the real value of 0.

There is your general rule.

>> No.5750509

>>5750502
Any Real times 0 is 0, I agree. In fact, any element of any Field times the 0 of that Field is 0. I agree there.

>> No.5750510

>>5750497
Do you know functional analysis?

>> No.5750516

>>5750510
I'm sorry. I'm just a dirty US Bachelors pleb, so I don't know offhand what you're talking about by name.

>> No.5750518

>>5750513
What is "retarded" about a rigorous mathematical definition? Because you are lacking the intellectual capacities to understand it?

>> No.5750519

>>5750493
I can into infinite strings perfectly, but I'm trying to sort out my answer, and everyone elses to avoid needless debate over what are essentially pedantics; everyone knows what we mean by 0.000...00001, but that meaning is discarded if you consider the information in the form of string literal, as a computer is wont to do.

>> No.5750521

>>5750518
It's retarded because there are a great many undergrads who honestly confuse the issue, and think that 0.00..001 is a distinct Real number from 0, who don't understand what a decimal expansion is, who don't understand the Cauchy construction of Reals. You are contributing needlessly to this confusion using a notation that no one else uses.

You are also a failure at commuting clearly you ideas. I knew the whole time what the hell you were getting at, but you were utterly unable to describe yourself. Instead, this wonderful anon:
>>5750508
had to come in and answer for you. You also need to work on your communication skills.

>> No.5750527

>>5750513
Actually, that is a rigorously defined mathematical definition; all I did was express it in string literal, since that was what you were asking for.

>> No.5750534

>>5750516
Do you know L^p spaces?

>> No.5750535

Going way back to the beginning of this whole shitstorm, you can see:

>>5750277
>because 0.000....1 as defined by the function that produces, matches the definition of 0

I don't know if that is the anon currently in the thread. I was responding to sentiment like that. My positions have always been:
- that's not a valid decimal expansion
- that's not a notation in use in any textbook or paper
- that's a horribly confusing notation, and a useless notation
- and I was asking for a formal definition which you were unable to provide, and instead some other anon had to go and do it. It wasn't much, just a sentence or two.

>> No.5750536

>>5750527
As a follow up, why do rigourous definitions need to terminate to count as rigorous definitions?

>> No.5750542

>>5750521
>there are a great many undergrads who honestly confuse the issue

You are projecting your own stupidity again.

>> No.5750538

>>5750534
Nope. I'm a pleb.

>> No.5750549

>>5750536
If you gave a definition whereby it involves converting one thing to another thing by a specified process, such as "reverse the digits", or some such, then it better be specified in a way that terminates, or else your definition is unusable.

I suppose it'd be possible to try and define "an infinite number of '0's followed by 1 '1'" and talk about reverse the ... whatever that is, and have this be doable in finite time, because in actuality we're just switching the two subsequences of the infinite '0's string and the finite "1" string.

It's just so removed from how everything else is defined though. I don't know offhand of any other such silly definition that involves talking about strings of infinite length and reversing them.

>> No.5750551

>>5750542
I don't know what you're talking about. I have been more than clear. That notation is never used in textbooks and papers, and if it were used in a class, it would be marked down.

>> No.5750552

>>5750535
>- that's not a valid decimal expansion
Nobody claimed it was. Nobody except you is talking about decimal expansions.

>- that's not a notation in use in any textbook or paper
Argument by authority is not math.

>- that's a horribly confusing notation, and a useless notation
Appeal to emotion is not math.

>- and I was asking for a formal definition
You were given the formal definition at least 5 times ITT.

>> No.5750556

>>5750551
>That notation is never used in textbooks and papers
That doesn't make it invalid. Any author can introduce new notations as long as they are consistent.

>and if it were used in a class, it would be marked down.
Not if it was introduced with its formal definition, as it has been done ITT.

>> No.5750557

>>5750552
>Argument by authority is not math.
Finally, we arrive at the critical point.

In this case, yes, it is, because it's not an argument over math itself, but an argument over notation. Over the meanings of symbols written down on paper. Over language. In that case, the only arguments you can make over the proper definition of language is argument from authority or consensus.

>> No.5750562

>>5750556
>That doesn't make it invalid. Any author can introduce new notations as long as they are consistent.
It's a stupid notation that doesn't add anything. There's absolutely no reason to add that notation. It's not a decimal expansion. It doesn't convert to any new or unique Cauchy sequences. It's utterly useless. It's also frequently used by those who have no clue about the Cauchy construction of Reals.

>> No.5750563
File: 18 KB, 300x300, haha lol.jpg [View same] [iqdb] [saucenao] [google]
5750563

>>5750538
>claims to have a BSc in math
>doesnt' even know L^p spaces

Holy shit. I'm studying psychology and even I know some basics of functional analysis.

>> No.5750566

>>5750563
>That's nice.jpg

>> No.5750568

>>5744030
It's true in the field of imaginary and complex numbers as well

>> No.5750569

>>5750556
>Not if it was introduced with its formal definition, as it has been done ITT.
It's been done only once, and not by you. It was done by the anon here:
>>5750508

>> No.5750572

>>5750557
>it's not an argument over math itself, but an argument over notation

The notation has been rigorously defined and shown to be consistent. There is nothing to argue. Your emotional dislike does not invalidate math.

>> No.5750573

>>5745261
/sci/ 17
math 0

>> No.5750575

>>5750549
what about the other way?

I took 1, and divided by 10 an infinite number of times.

Plenty of other irrationals can be defined using infinite series, why would division be any different?

>> No.5750578

>>5750572
I agree. There is now a rigorous definition. Not provided by you. I asked you to provide it for many posts, and was unable or unwilling to. Now someone else has, and I agree it's well defined. It's also stupid and useless. This isn't emotional. It's a rational analysis of the utility of the new syntax.

>> No.5750579

>>5750562
>It's a stupid notation that doesn't add anything
That's just your opinion and math doesn't give a fuck about your opinion. At this point I seriously cannot tell anymore whether you're a very dedicated troll or an anti-intellectual autist. In both cases please stop posting.

>> No.5750583

>>5750575
The definition of limits as n->infinity is never defined as an infinite process, unlike what you tried to do.

>> No.5750585

>>5750579
It's not just an opinion. It's a demonstrable statement about the utility of the new notation.

>> No.5750586

>>5750569
>It's been done only once, and not by you. It was done by the anon here: >>5750508
He only repeated what I stated several times. Don't blame your illiteracy and your coginitive impairment on me.

>> No.5750592

>>5750586
Please point out where you defined what he said in the same clear and precise terms. Perhaps I missed it.

>> No.5750597

>>5750578
>There is now a rigorous definition. Not provided by you

I said the exact same thing a hundred times. The fact that you suddenly accept it after another poster repeated it only shows us how immature you are. You value facts by the person who presents them. That's extremely childish and anti-intellectual.

>> No.5750603

>>5750583
>The definition of limits as n->infinity is never defined as an infinite process

0/10

>> No.5750604

>>5750597
Please point out the posts where you think you said something equivalent so I can reexamine my position, because I don't remember anything like that from you, and I am not going to reread the whole thread, and I would prefer to argue over contents of a specific post instead of nebulous whole thread.

>> No.5750609

>>5750583
I guess that makes sense.

>> No.5750611

>>5750603
It's not. For rational-valued sequences, for example, lim n->inf is defined in terms of the usual epsilon definition, not in terms of an infinite process. This is one of the stumbling blocks of calc 1.

>> No.5750607

>>5750585
It is your opinion. Math works independently of whether you like it or not.

>> No.5750614

>>5750592
>>5750604
I explained it when I gave you the definition. It's time for you to stop posting. You were shown to be wrong and retarded. Instead of being thankful for the lesson you are now behaving like an emotionally hurt toddler. Please come back when your mental maturity has left the level of a kindergartener.

>> No.5750615

>>5750607
I agree your notation, with the formal definition provided by someone else, is rigorous and usable. It's also demonstrable useless, because there is a shorter notation that encompasses everything your notation does, and is better in every way, and your notation adds nothing on top of the existing notation. That's the textbook definition of "useless". This is objective, demonstrable fact.

>> No.5750620

>>5750614
Again, post link please.

>> No.5750623

>>5750611
Those are the same thing.

>> No.5750626

>>5750615
>with the formal definition provided by someone else

Your emotional bias is truly astounding.

>> No.5750627

>>5750623
No, they're really not. One leads to people saying "0.999... gets closer and closer to 1, but never reaches". The second leads to demonstrable, verifiable, finite(!) proofs that 0.999... equals 1.

>> No.5750630

>>5750620
Read the thread. See where the notation has been defined.

>> No.5750632

>>5750626
Your inability to substantiate your own claims with a simple post link, and instead resorting to insults, is telling.

>> No.5750635

>>5750627
>One leads to people saying "0.999... gets closer and closer to 1, but never reaches".

No, that's just your idiocy. Don't blame your failure of understanding on others.

>> No.5750642

>>5750635
The epsilon proof does not refer to a non-terminating Turing machine. Instead, it refers to a finite-length well-formed symbolic logic definition, aka the usual epsilon definition.

This is fundamentally different than earlier where you said that I need to reverse an infinite length string.

>> No.5750648

>>5750632
In my very first post ITT I gave you the rigorous definition. You not only failed to understand it but you even anti-intellectually denied it and refused to consider what it means. With that attitude you're not gonna get far. Maybe you took some number crunching classes in your community college, but for sure you are never ever gonna do any kind of rigorous proof based math.

>> No.5750655

>>5750648
Because you're posting anonymously you're going to have to provide a post link please.

>> No.5750659

>>5750642
Nobody except you is talking about Turing machines. It happens very often in math that limit processes are described algorithmically.

>> No.5750662

>>5750642
For example, do you know what a computable (Real) number is?

A computable (Real) number is a Real number so that there exists a Turing machine TM so that for all decimal places N, there exists finite time T so that TM run for T will produce accurately the first N decimal digits of the Real number.

>> No.5750668

>>5750659
Not really, no. Maybe in a calc 1 intro, to ease the students into the formal definition, but it's not the formal definition. You won't find that shit in any published papers, and most likely not in any advanced textbooks either.

>> No.5750670
File: 177 KB, 736x689, is this guy serious.png [View same] [iqdb] [saucenao] [google]
5750670

>Scientist !!ThFjnJh4EkH

>I have BSc in math
>I don't know L^p spaces
>I don't understand real analysis
>I don't even understand limits
>I can't even read

Watch out guys, we're dealing with a master ruseman over here.

>> No.5750674

>>5750670
Part of that is accurate, yes, and part of it is wrong. Sorry that my classes didn't include those topics and I focused on other topics.

>> No.5750677

>>5750668
Do you know differential topology?

>> No.5750680

>>5750677
I am not going to answer your dick-waving questions any more as it seems you only intend to make pitiful attempts at trolling me with the answers, as opposed to making genuine honest conversation.

>> No.5750676

>>5750659
You were talking about Turing machines the moment you asked me to reverse a string, infinite length or not.

Or do you not accept the Church Turing thesis?

>> No.5750686

>>5750676
1. That poster talking about reversing an infinte string wasn't me.
2. Reversing an infinite string does not require a Turing machine. It's sad to see how you cannot think outside of a very few and very limited concepts you are mindlessly and dogmatically applying to everything to see, no matter how inappropriate they might be.

>> No.5750692

>>5750686
>2. Reversing an infinite string does not require a Turing machine.
So, you reject the Church-Turing thesis?

>> No.5750695

>>5750686
>>5750692
Or have you found some other method of computation that isn't equivalent to Turing machines or lambda calculus?

>> No.5750705

>>5750680
I'll take that as a "no". My intention is not "dick waving". I don't even have a dick. You were talking ignorant nonsense and if you took any kind of higher math classes you'd realize why you were wrong. You are disproportionally proud of your real analysis class. Even though it might make you a little bit more knowledgable than the average high schooler, you are far far away from knowing, let alone doing, actual math.

>> No.5750711

>>5750705
Yes yes. Go dick wave, and say I'm too stupid to understand because I don't understand this entirely unrelated concept.

Notice how you keep insulting me without providing anything of substance, despite my pleasant asks for stuff with substance. Notice how I've provided definitions on demand for all the terms I've been using.

>> No.5750713

>>5750692
>>5750695
Who said it has to be computable?

>> No.5750722

>>5750713
I asked for a method by which I could convert your String literals to a Cauchy sequence of Rationals, aka to a Real. The process damn well better be computable and finite.

>> No.5750727

>>5750711
If you had the necessary background in undergrad math, we could have a had a better conversation. In the context of L^p spaces a much more concise and formally correct definition resolving your misunderstanding would have been possible. Unfortunately despite your claim of having a BSc in math you seem to be ignorant of concepts approachable even by laymen.

>> No.5750728

>>5750722
To be specific, a way to convert between your notation and any of the commonly used notations for describing a Real. Which should be doable if you claim that it is 0.

>> No.5750729

>>5750727
Try it on me. Explain how 0.00...001 has any use in L^p spaces.

>> No.5750746

>>5750729
Use? Now after accepting its correctness you are only attacking its usefulness? You claim to study math but you're valuing it by its usefulness? I guess you'll refuse to take any higher math classes then because "hurr durr useless". Pure anti-intellectualism.

>> No.5750753
File: 70 KB, 307x315, top lel.jpg [View same] [iqdb] [saucenao] [google]
5750753

Let me get this straight: This "scientist" tripfag thinks he's the greatest mathematician of all times after taking babby's first analysis?

my fucking sides

>> No.5750754

>>5750746
I have more than abundantly clear on this issue, and have not wavered from this position.

1- It is not a decimal expansion.
2- I asked for a formal definition for its meaning, which someone else eventually provided.
3- It's a notation which has no role or utility over existing commonly used notations, and should not be used. It should not be used because it adds no utility, and is longer than existing notations with no added benefits or descriptive value.

>> No.5750756

>>5750753
Nope. I'm pretty sure I'm just a pleb.

>> No.5750758

>>5750754
>1- It is not a decimal expansion.
Nobody claimed it was. You were the one inappropriately mistaking it for a decimal expansion.

>2- I asked for a formal definition for its meaning, which someone else eventually provided.
Then what's your fucking problem?

>3- It's a notation which has no role or utility
Just your uneducated and irrelevant opinion.

>> No.5750765

>>5750758
Are you poster:
>>5750212
?
Because that poster disagreed with me, and started this whole shitstorm.

>> No.5750772

>>5750758
>>1- It is not a decimal expansion.
>Nobody claimed it was.
To be clear, clearly someone did:
See: >>5750212

>> No.5750777

>>5750765
>>5750772
Where did >>5750212 say anything about "decimal expansions"? I said "defined as a limit". Decimal expansions are not the only objects defined as limits. Thanks for displaying your illiteracy again.

>> No.5750782

>>5750777
I made a simple claim that it was not a decimal expansion, and that other poster rudely corrected me, strongly implying that it is a decimal expansion. In effect strongly implying that I am mistaken.

Your naive literal reading ability is amazing. You called me autistic. Are you just projecting? Come on man. The guy clearly implied I was wrong when I stated it was not a decimal expansion, which is the same thing as strongly implying that it is a decimal expansion.

>> No.5750784

>>5750729
That inevitably leads to the question of whether you're familiar with basic notions of measure theory and Lebesgue integration. Are you?

>> No.5750786

>>5750784
This inevitably leads to the question of whether you're going to get to something resembling a point instead of dick waving.

>> No.5750789

>>5750782
>I made a simple claim that it was not a decimal expansion
That claim was unnecessary because we weren't talking about decimal expansions the way you defined them.

>and that other poster rudely corrected me
Of course I correct blatant idiocy when I see it.

>strongly implying that it is a decimal expansion
Please show me where I implied this. I was telling you that we were talking about limits, not decimal expansions.

>> No.5750794

>>5750786
Where am I "dick waving"? You want me to explain something. Before I can do so, I'll need to know what your background is. You have to be familiar with terminology and basic theorems. There is no "dick waving". It's undergrad babby math. If I wanted to "dick wave", I'd post about research math.

>> No.5750798

>>5750727
>In the context of L^p spaces a much more concise and formally correct definition resolving your misunderstanding would have been possible.
What? Lebesgue spaces aren't about arbitrarily re-defining notation dating back to 600 A.D.

>> No.5750799

>>5750789
>That claim was unnecessary because we weren't talking about decimal expansions the way you defined them.
There's no other way to define them. That's the definition in every textbook.

Some other poster properly stated that the notation is bullshit here:
>>5745238
Several idiots took issue with that generally correct statement. The notation is bullshit. While you may define it to mean something, which someone else did for you much much later, at the time, no one gave a definition for that, and the proper reply at the time was to note that it is malformed, and does not denote a Real Number.

Someone took issue with this claim, and said I and the other poster was wrong, and that it does denote a Real Number. Under the usual conventions, it does not, and it's malformed.

This is all I have been talking about in the thread for the most part, though once you extended the notation, I've also been arguing that useless, has no utility, is stupid, and is needlessly confusing to undergrads and new people, such as might be on /sci/.

>> No.5750801

>>5750789
>Of course I correct blatant idiocy when I see it.
So, that was you who "corrected" me when I said it wasn't a decimal expansion? Because that makes you simply and clearly wrong. It is not a decimal expansion.

>> No.5750808

>>5750799
>There's no other way to define them
Your stupidity is painful.

>stated that the notation is bullshit here:
He just didn't understand the notation. Given its definition he actually claimed that 0 doesn't exist. Obvious nonsense.

>The notation is bullshit.
It has been defined rigorously.

>> No.5750812

>>5750801
>It is not a decimal expansion.

That's what I told, you incompetent dimwit. YOU are the one who keep insisting that it has anything to do with decimal expansions. It doesn't. It is defined by a limit and does neither require nor imply the notion of decimal expansions. How many times do I have to repeat myself? How severely disabled are you?

>> No.5750813

Please, i implore you all to stop bumping this thread.
The number of retarded "prove me wrong" threads on the front page is causing me distress.

>> No.5750816

>>5750812
I understand your position just fine.

If I was correct, you shouldn't correct me.

When that poster said that 0.00...001 is malformed under the usual conventions, you should support that poster instead of "correcting" them.

When I said that it is not a decimal expansion, you should say "you are correct, although by a completely non-standard extension of the syntax, we can make something well defined out of it".

You did neither.

>> No.5750818
File: 27 KB, 300x330, duty_calls2.png [View same] [iqdb] [saucenao] [google]
5750818

>>5750813
Sorry. I'll be off to bed shortly.

>> No.5750820

>>5750816
That's what I did. Don't blame me for your lack of reading comprehension.

>> No.5750821

The answer is clearly y = 1 - 0.999...

>> No.5750823

>>5750818
I sure hope so. Please die in your sleep.

>> No.5750824

>>5750820
That's clearly not what you did. You insinuated that I was wrong, that the notation is commonly used and well-defined under the common conventions. The facts of the matter are that the notation is malformed under the common conventions, and would likely get you laughed at if you tried to use it in any paper or textbook.

>>5750823
Such hate.

>> No.5750829

>>5750824
>You insinuated that I was wrong, that the notation is commonly used
I didn't. Again you fail at reading comprehension.

>and well-defined under the common conventions
The "common conventions" include reading and understanding an author's definitions of notation before mindlessly attacking the notation under false premises.

>malformed under the common conventions
As it has been pointed out it is not malformed.

>Such hate.
You're right. You don't deserve hate. You're probably an autistic virgin whose only enjoyment stems from being an overly emotional asshole "troll" on the internet. Go ahead and keep being bragging about your babby real analysis cousre. That's probably the only thing you have. Very sad.

>> No.5750834

>>5750829
You didn't even attempt to provide a formal definition at the time that you "corrected" me and the other posters who rightly pointed out that the notation was malformed under the common conventions.

You are an asshat who is unable to admit that you are wrong. I think I am done with this thread, as it seems we've gotten to the point of contention, and you're unwilling to budge further.

Good day.

>> No.5750837

>>5750834
>You didn't even attempt to provide a formal definition at the time that you "corrected" me
The definition has been posted yesterday ITT, long before you came here to derail the thread with your ignorant garbage.

>You are an asshat who is unable to admit that you are wrong.
Nice projection. This sentence perfectly describes YOUR problem.