/sci/ - Science & Math

>>5945332

>>5945335

>>5945337

>>5945340
This is my gift to /sci/. Use it wisely.

>>5945380
tl;dr

>>5945392
>impossible to read

nigga you blind

if i shit on your porch and call it a gift can you use it wisely?

seriously these things are impossible to read, make the back grounds less intrusive and i might read them

Dude this is cool. Good job.

Good shiat bro, but it isn't going to stop trolls

I liked the explanations, thanks.

The first one is easy to read but not the others.

I hope you can remake it so I can read it all.

This should be pinned.

>>5945332
Thank you. Thank you so much.
If only we could be sure that the fags who normally post the shit you've addressed read this.

>>5945440
Which parts are difficult to read? It seems clear to me.

In a perfect world, we would use this opportunity to elaborate a precise list of all such items and compile a small collection of articles with proper Tex formating.

We could use them as a starting point to ellaborate a collective textbook where in each chapter, a layman introduction could be presented (in a similar fashion to what we have here) and the second part could be a rigorous structured, solid presentation of the subject matter.

We could, this way, create a Bourba/sci/ collaborative author and write some pedagogical yet solid mathematics. We can have some anons working on trigo while others would work on topology.

We'll create our own Standard text. We could even enrich it with a dictionary of exotic proofs to all the theorems presented and an explanations of mathematical trivia, even a bit of epistemology and history.

A man can dream.

>>5945451
It wouldn't matter. Almost all the time they are either trolls or dumbasses who pretend to want discourse but really just expect to show us the light. The few people these would work on, those that honestly just don't know or understand these concepts aren't a problem.

Tripfag get off my /sci/

>>5945332
>.9999... = 1

>>5945457
This sounds like it would end in a lot of people arguing, but I wish it could happen. Bourbaki sucks though.

>>5945459
The point is guides like these help reveal the real trolls. After these are posted, anyone who keeps replying is an obvious troll; meanwhile anyone who wants to actually learn can read them and understand.

I have updated 1,3, and 4 for myself with some spelling corrections/clarifications. Anyone see possible improvements on 2?

>>5945476
dude more than one person has posted that its hard to read. change the back ground to white and the text to black. who the fuck needs random space artwork behind words? fuck

>>5945483
I can make a plain white background version if you'd like.

>>5945509

>>5945515

>>5945517

>>5945518

the hero /sci/ needed

something of this ilk has been long overdue

Fixed more nitpicking mistakes in 2 and 4. Any suggestions/corrections should be posted in the thread. Thanks for the accolades everyone; I've been wanting to do something like this for a while.

Hopefully /sci/ can begin discussing real mathematical questions after these trivial squabbles are settled.

>>5945518
Wait, some people on this board actually thought of infinity as a number?

>>5945335
You should make it more clear what the notation R/{0} means, as it could easily confuse someone who is already struggling to understand.

>>5945586
not at all, its implying having to direct someone to basing their 0

>>5945586
You mean R\{0}? I think it's standard notation.

>>5945588
What does this even mean?

>>5945623
> >>5945588
Basing your base 0 is healthy for your mathematical growth, lot of work to be done in the field though

>>5945666
>Basing your base 0

Please stop speaking gibberish and post some definitions?

>>5945332
well that's a worthless guide, hard to read and the entire thing is using flawed logic lol, wtf

>>5945337
>>5945335
>>5945332
and no math was performed that day

>>5945380
pretty good op but i am colorblind, can you make a colorblind readable version.

>>5945332
>arguing with Cauchy construction about facts about the decimal construction

retards, retards everywhere

>>5945332
1) Wrong equivalence relation and wrong construction retard
1c) No you're using rational retard

>>5945678
The standard equivalence relation is <span class="math">a_n ~ b_n[/spoiler] if <span class="math">\lim_{n\rightarrow \infty} a_n - b_n = 0[/spoiler].

Using rational what?

>>5945680
a_n ~ b_n

>>5945675
See the white background posts above.

>>5945672
>>5945673
>lel this sucks im so smart

>>5945680
rational number

The standard equivalence relation is: if there exist an n in N such that for all m>n a_m=0 and a_n=/=0 then a_i~b_i with b_m=9 for m>n and b_n=a_n-1 (accounting for carry) and the rest equal

0.999...=/=1. This is the most pointless thing to say ever. Numbers are infinite and 0.999 is infinitely close to 1 but the fact of the matter is that it isn't 1. Fortunately, only autistic people like you care about that infinitely small difference.

This is a really good explanation. It should help even the most stubborn idiots to understand.

is it sceince?

>>5945803
did you just make that quote up?

>>5945840

1/3 = 0.333...

3*(1/3) = 3*(0.333...) = 3/3 = 0.999... = 1

Also if 0.999... =!= 1
Then you're saying theres something in between. Say zero point an infinite nines plus another one. But that's not how infinite works, because then you didn't have infinite point nines in the first place.

>There is no 0.000.0001
Wrong. This notation makes perfect sense. If 0.999... is another notation for 1, there is no reason why 0.000.0001 shouldn't be another notation for 0. It is easily and consistently defined as the limit of (0.1)^n as n approaches infinity.

>Infinity is not le number.
Wrong. Please show me the mathematical definition that says "numbers" have to be elements of a field.

>There is no 0.000...0001
Wrong. This notation makes perfect sense. If 0.999... is another notation for 1, there is no reason why 0.000...0001 shouldn't be another notation for 0. It is easily and consistently defined as the limit of (0.1)^n as n approaches infinity.

>Infinity is not le number.
Wrong. Please show me the mathematical definition that says "numbers" have to be elements of a field.

Why are you intentionally spreading misinformation?

>>5945340
Regarind pi. Also just because something keeps going forever, doesn't mean everything will come up or happen.

That's like saying somewhere in pi's decimals, if we decypher them to the english language through some algorithm, it proves god. Later digits decyphered then disproves god.

Eternity doesn't work the way our brain want it to.

The pictures are cringeworthy. I seriously cannot tell whether OP is a pseudo-intellectual high schooler who misunderstood basic mathematical concepts or whether he's just another shitposting troll.

>>5945875
Well he started a 0.999...=1 thread
At least in my books thats shitposting troll, but i presume there is a more than enough dose of pseudo-intellectualism in there too.

But at least we all agree it's cancer.

>>5945875
What's wrong with them?

>>5945887
See >>5945865

>>5945865
>defined as the limit of (0.1)^n as n approaches infinity

Why?

You are the hero /sci/ needs but does not deserve.

>>5945911
For the same reason 0.999... is defined as the limit of <span class="math">\sum_{k=1}^n 9\cdot\left( 0.1\right)^{k}[/spoiler] as n approaches infinity.

>>5945916
No, he's just a psuedo-intellectual fucktard troll.

>>5945917
What reason?

>>5945337
I take issue with your explanation of an infinite limits. You just gave the definition for finite limits. And using that definition directly to try and understand inifnite limits, would be done by pretending L was infinity, which would be like pretending infinity is a number which is contrary to the point in this paragraph, making the message confusing.

What I mean to say is you should simply have supplied the definition of an infinite limit. That limit x -> infinity f(x) = infinity if for all M there exists a d such that for all f(x) > d, f(x) > M.

>>5945332
>Cauchy sequences are defined using real numbers
You were doing so well.

Informative.
Thanks, OP.

>>5946082
Stop samefagging. The stupidity of your troll pictures has been pointed out more than once ITT.

>>5945865
The limit of (0.1)^n as n goes to infinity is 0. As explained, the notation makes no sense. How can you have infinite zeroes, followed by anything? It is self-contradictory to say "infinite with something after it." There is no "after it" by premise.

>>5945865
I was obviously adopting the standard intuitive feeling of a number as an element of the familiar complex numbers, but I addressed the possibility of adjoining "infinity" under certain circumstances.

>>5945874
I said that by stating Pi was not even proven to be normal. The statements after the hyphens are the misconceptions, followed by the explanation.

>>5945917
That one makes sense, and that limit is 1 (another way of proving it).

>>5946035
I gave the definition for limits as x goes to infinity, but didn't want to get into the topic of infinite limits.

>>5946042
Sure, you could let <span class="math">\epsilon > 0[/spoiler] be any rational number and do it that way, but the standard completion in topology is to use the real number system for your <span class="math">\epsilon[/spoiler]'s. But then there's the issue of showing that the rationals are dense in the reals to demonstrate that this is in fact an equivalent premise, and I didn't want to get into that.

These guides were meant to be for someone at the high school/year 1 level as stated.

>>5945860

Suppose you do find a number in between. The one's place must be 0, else not in between. Tenth's place must be a nine. Same for hundreth's, etc. So the only possible number in between is .9 repeating, which isn't greater that itself, which means no numbers in between.

>>5946098
>As explained, the notation makes no sense.
Are you retarded? In the post you're referring to I explained why the notation DOES make sense.

>the standard intuitive feeling of a number
In other words you're talking out of your ass.

>>5946231
If you define it as "the limit of (.1)^n as n goes to infinity" then you are defining it to be zero, as that is the limit. Why the hell would you make retarded notation just to define it to be zero?

>>5946278
>Why the hell would you make retarded notation just to define it to be zero?

Why the hell would you use the retarded notation 0.999... instead of writing 1?

>>5946290
Nobody does. Whenever the notation is seen, it is quickly replaced with 1. Nobody ever writes .000...1 because it's idiotic.

>hurr let's make infinitely many zeroes then attach a 1 to the end even though there is no end!

0.999... = 1
0.998... = 0.998...
0.997... = 0.997...
0.000...1 = 0
0.000...05 = 0
0.000...04 = 0
0.000...03 = 0

http://qntm.org/pointnine is still the best list of proofs that 1=0.999...

On that note, OP, do you have a pastebin of the raw text? That would be helpful to me. Thanks for this!

>>5946311
INFINITE PROOFS OTHERWISE INNNFFFIINIIIITEEEEEEEEEE GO L2QMBITCH

>>5946294
What part of my explanation for the notation did you not understand?

>>5946325
Explain what 0.000...1 means. There is no room for a 1 after infinitly many zeroes, because, you know, there's infinitely many of them.

>>5946333
It is the limit of (0.1)^n as n approaches infinity.

>>5946338
>the .
>huehuehuehueheuheuheuheuueuheuehuheuhehue

>>5946333
Explain what 0.999... means. It doesn't make sense. You cannot have infinite 9s after the decimal point. You could never write down such a number or do math with it.

>>5946338
So you made a self-contradictory notation for 0?

Wow, someone grab the Fields Medal.

>>5946354
0.999... = <span class="math">\sum_{n=1}^{\infty} 9(.1)^n[/spoiler]

>>5946355
How is it self-contradictory? It is mathematically consistent.

>>5946359
Infinity is not a number, you retard.

>>5946355
So you made a self-contradictory notation for 1?

Wow, someone grab the Fields Medal.

>>5946359
So this limit exists but the limit of (0.1)^n for n to infinity does not exist? Can you post a quick proof or something?

>>5945571
So we're allowed to think of all points on the sphere as a number but that one? Seems silly to me.

>>5946396
You can't write 0.000...1 as a sum in standard decimal notation, while you can with .999... as displayed above.

Well, this thread has degenerated into trolls trolling trolls.

>>5946420
Who cares if you can write it as a sum? Are you too stupid to understand how the notation is defined?

>>5946417
>wanting the real numbers to be bounded
>wanting a non-archimedean field

What are you, a number theorist faggot?

>>5946423
Fine, if you want to conjure up the symbol "0.000...1" and define it to be zero, go ahead. Mainstream mathematics does not adopt this convention, however you are welcome to sit in your own little world playing with your own trivial constructions.

>>5946425
Well, I'm into geometry mostly, so I gauss number theory comes naturally with that.

>>5946429
I'm just demonstrating that idiots like you are retarded. You go scream "hurr durr u cannot hav a 1 after infinte 0s so its le wrong xD i'm such a euphoric genus." I demonstrated that this appeal to preschool math misconception is not valid reasoning in real math. The notation can be rigorously defined and it turns out that a number with infinitely many zeros happens to be another notation for 0 the exact same way and with the exact same reasoning you accept for why 0.999... is another notation for 1.

A correction to image four on pi and normality:

A normal number is one where every sequence of digits occurs with equal probability in every base. However, pi could only have this property for one base, and, if written in that base, would have the required encoding of any digit string required at some point. For example, the Champwenowne constant (en.wikipedia.org/wiki/Champernowne_constant, can't post it since it makes 4chan think the post is spam) has this property in base 10, but it is not necessarily normal with respect to any other base, so is not generally a normal number. But, since it has every digit sequence in order, the Champernowne constant clearly encodes all of Shakespeare or whatever you want it to have.

But that's not all. Imagine a number in base 2 where the digit 1 occurs exactly twice as frequently as 0. This number is not normal in base 2, since the digits do not occur with equal probability, and may not be normal in any base. However, it could still contain every digit sequence somewhere, just not with equal probability. So the concept of normality isn't necessary for having every digit sequence in it (though it is indeed sufficient).

>>5946438
Thanks, you've inspired me. I'm going to make up a definition of my own!

<span class="math">4.1 := \lim_{x\rightarrow 4.1} x[/spoiler]

Wow, so rigorous I'm using limits like a pro! So advanced and genius thanks!

>>5946438
Yeah, except real numbers in a given base b are defined to be expressions of the form <span class="math">\sum_{n=k}^{\infty} \frac{a_n}{b^n}[/spoiler] for some integer k. 0.999... can be represented in this form, yet your number cannot.

Checkmate atheists.

>>5946469
This is not how the real numbers are defined.

>>5946473
>real numbers are not all convergent cauchy sequences of rational numbers

top kek

>>5946481
>the sequence (0.1)^n is not a convergent cauchy sequence of rational numbers

Cool story, retard.

>>5946485
Now express it as a sum in base 10.

Why do I even bother with the trolls?

>>5946490
>Now express it as a sum in base 10.

Why would I do that? Because that's the only representation you learned in first grade of primary school?