0.9999... != 1

[Anonymous No.11547504]

Why do we still allow the never-explained "go-to-infinity" step to be applied to simple notations like 0.99999...? Who the fuck told you you could just "go-to-infinity"? Oh gees, I guess we can just do whatever the fuck we want in mathematics right, just GO TO FUCKING INFINITY, I MEAN IT'S OBVIOUS RIGHT??? INFINITY IS ALL AROUND US. 0.99999..... is just one, I mean, why wouldn't it be? Who the fuck cares about the 0.00000.....0001? I guess we can redefine e=3=pi as well. Makes things easier, eh? That's what we do, as mathematicians.

Pff. 0.9999... is not 1 and never will be.

[Anonymous No.11547508]

>another 0.9999... = 1 thread
How many of these threads are we going to have?!
fucking stop this madness

[Anonymous No.11547512]

>>11547504
Because that is the definition of real numbers and 0.999... explicitly involves an infinity step already.

[Anonymous No.11547515]

>>11547504
>>11547508
>>11547512

The inability many people today who view themselves as being "scientific" as well as math fans (left-brain prisoners) have in comprehending that .999 isn't the same as 1, is completely connected to their inability to grasp eternity and infinity. Their minds have basically been programmed to believe eternity and infinity are impossibilites. Over the course of the last 10 or so centuries of indoctrination into an alien world-view, they've "learned" to be unable to comprehend it.

This difficulty they have with eternity/infinity shows up in many different fields, from math to astrophysics.

This mental handicap is inherited directly from the (((Abrahamic))) religions, more specifically Christinsanity for us Westernerns. In it's origin, the inability to understand infinity and eternity is 100% Judaic in thought/philosophy. In contrast, the non-Jewish man; the Pagan man, at least the /European/ Pagan man, never had any problem with infinity and eternity. Christinsanity introduced into the minds of people the idea of life and the world/universe being linear, starting from point A and ending with a point B, whereas in the Native European world-view everything is infinite, a circle.

That's why many people today can't understand that .999 repeating forever will never reach 1 -- they refuse to accept the idea of an infinite/eternal repetition. Saying "it's 1" is their method of escaping from the uncomfortable (and to them insurmountable) challenge which the concept of infinity/eternity is to their Judaically-induced mental disease.

[Anonymous No.11547520]

>>11547515
>999 repeating forever will never reach 1
There you are right, since 0.999... and 1 are just different symbols for the exact same thing you really can’t say they “reach” one another.

[Anonymous No.11547524]

>>11547520
9s repeating forever after 0 will never be equal the whole number "1". No matter how many 9s are used. Even when the amount is infinite. It will always be less than 1, forever.

[Anonymous No.11547528]

>>11547512
>Because that is the definition
Yeah, well, WHY is it the fucking definition?

You're like fucking religious fanatics.

NOOO YOU CAN'T JUST ASK QUESTIONS LIKE THAT, MY BOOKERINO DEFINITIONS SAY SO!!!11!!

[Anonymous No.11547532]

>>11547524
They are by definition different symbols for the same thing.

It doesn’t mean anything more then saying 1/2 =2/4 both are just different symbols for the same thing, by definition.

[Anonymous No.11547537]

>>11547520
0.999... is a static object, there's nothing "growing" anywhere - all the 9's are there from the get go.
lim-fiddling is a different beast altogether, there it makes sense to talk about something growing

[Anonymous No.11547539]

>>11547528
>eah, well, WHY is it the fucking definition?
Because it lead to a very useful and coherent theory of real numbers.

> You're like fucking religious fanatics.
There are is an extremely wide variety of different numbers and definitions.

> NOOO YOU CAN'T JUST ASK QUESTIONS LIKE THAT, MY BOOKERINO DEFINITIONS SAY SO!!!11!!
Mathematicians asked those exact questions for about 2000 years and continue to do so.

[Anonymous No.11547540]

>>11547524
>repeating forever after 0 will never
helloo-o, it's not a diesel engine chugging along, with a clock ticking inside

[Anonymous No.11547544]

>>11547508
desu i just saw how many replies the other 0.999... != 1 threads got and I'm lonely and depressed so I just want some (You)s (._.)

[Anonymous No.11547545]

>>11547537
Yes. 0.99... is just a different symbol for 1.
There indeed is no growing, it’s just two different symbols for the same thing.

[Anonymous No.11547547]

>>11547508
>fucking stop
stop the corona and people will have other things to do

[Anonymous No.11547548]

Two proofs 0.999... = 1

Via Cauchy sequences:

0.999... = (0.9, 0.99, 0.999,...) = lim as n-> inf of 1-1/10^n = 1

Via Dedekind cuts:

Assume to contradiction that x is a rational number such that

0.999... < x < 1

0.999... is greater than any finite string of 9s so for any natural number n

1-1/10^n < 0.999... < x < 1

1-x < 1/10^n

10^n < 1/(1-x)

n < log(1/(1-x))

Let n = ceiling(log(1/(1-x)))+1

ceiling(log(1/(1-x)))+1 < log(1/(1-x))

This is a contradiction, so x does not exist and 0.999... = 1.

[Anonymous No.11547549]

This entire thing comes down to the fact that there is no such thing as 0.000...001 this is not a thing that exists because you can't have an infinite amount of zeros and then a 1 at the end that terminates it because then the string of zeros isn't infinite anymore.
Everyone who says .99999... =/= 1 continues to be confused by this.

[Anonymous No.11547550]

>>11547539
>Because it lead to a very useful and coherent theory of real numbers.
Yeah? How so?
I've turned into an ear. Cmon. Explain to me, from bottoms up, why exactly does 0.999... != 1, without invoking your divine scriptures. If you're introducing a definition, explain why is it valid and why should it be accepted that way.

[Anonymous No.11547554]

>>11547504

0.999... DOES NOT EQUAL 1

You are doing God's work, Anon. I know declare the RECONQUEST of Mathematics for the FINITE UNIVERSE! DEUS VULT!

Soon we will bring these GODDAMNED heathens to their knees, a position they should be well adapted to after all their years of OUTRAGEOUS SODOMY!

[Anonymous No.11547562]

>>11547554
good lord, your penis must be small.
the scream-compensating is embarrassing to witness.

[Anonymous No.11547564]

>>11547549
>This entire thing comes down to the fact that there is no such thing as 0.000...001 this is not a thing that exists
>But muh infinity exists.
This is the state of Maths.

[Anonymous No.11547568]

>>11547550
>Yeah? How so?
Modern analysis is the basis for almost all human progress.
For analysis you need real numbers.

> Explain to me, from bottoms up, why exactly does 0.999... != 1
That takes about 10 hours and a few dozen 4chan posts, it is explained in many books totally from the bottom up.
Read them.

> If you're introducing a definition, explain why is it valid and why should it be accepted that way.
Every definition is a priori valid. I think you mean axioms.

> without invoking your divine scriptures.
There is no divinity in them. They are books, they explain things. Different books disagree on methods, contents and definitions .

[Anonymous No.11547572]

>>11547554
Glad to hear another voice of reason, anon.

Infinity was just a made-up concept to simplify the "we can go like this however long we want", like when you're searching for a number that, when squared, equals 2. Sqrt(2) doesn't exist, all that exists is a bunch of numbers that can get close to it.

But lazy mathematicians just HAD to forget where they came from. "NOO SQRT IS A ~REAL~ NUMBER - I MEAN I CAN DRAW IT IN MY HEAD THAT MEANS ITS REAL!!!~~" argument simply doesn't hold water.

And then other mathematicians forgot that those idiots just used "infinity" as a shortcut, and started making up shit about infinity. Suddely, everything is an infinity. That nigga Cantor even thought infinity was a number. What the fucking fuck.

You retards are just making shit up, I swear. No wonder you don't get any funding at all. You don't deserve that shit.

[Anonymous No.11547575]

>>11547564
infinity is a concept.
000...1 is just a syntax error

[Anonymous No.11547577]

>>11547564
Yes, infinity exists and is well defined.
In fact, you must claim that infinity exists in order to claim that there might exist an infinite amount of zeros and then a one that somehow terminates (which is a contradiction of course, the infinite amount of zeros does not terminate as it is infinite).
Nothing about this is contradictory or confusing or difficult to understand

[Anonymous No.11547579]

>>11547572
>Infinity was just a made-up concept t
everything in math is

[Anonymous No.11547583]

>>11547572
>Infinity was just a made-up concept
Every concept is made up.

> Sqrt(2) doesn't exist
It exists like the Color red exists.

[Anonymous No.11547584]

>>11547568
>it is explained in many books totally from the bottom up.
No, it's not. It's only demonstrated and given as if it was a fucking Sacred Scripture. And I can't communicate with a book, I can't ask it why a concept is valid. I can't criticize it. It's literally the Sacred Scripture for you faggots.

>Every definition is a priori valid
You know what I mean, you Kantian faggot. Semantical validity and conceptual validity are two different things.

[Anonymous No.11547585]

>>11547572
The square root of two exists just like 2 itself exists

[Anonymous No.11547586]

>>11547572
>Cantor even thought infinity was a number.
[citation needed]

[Anonymous No.11547591]

>>11547584
>No, it's not.
There are dozens of book deriving the real numbers from ZFC.

>>11547584
>It's only demonstrated and given as if it was a fucking Sacred Scripture.

> It's only demonstrated
No, it is either accepted without evidence, like ZFC or proven.

> You know what I mean
I do not.

> I can't ask it why a concept is valid. I can't criticize it.
Ask in /sqt/ and somebody will respond.

[Anonymous No.11547595]

>>11547586
Ordinals is what he means, I think

[Anonymous No.11547604]

>>11547591
>There are dozens of book deriving the real numbers from ZFC.
Yeah, like there are dozens of *book* deriving the existence of God from the ancient scriptures. It doesn't mean SHIT.

If you're gonna keep dodging the question and calling upon your sacred scripts, get the fuck out of my thread you fucking fanatic.

>>11547585
Bullshit. I can have two rocks. I can't have exactly sqrt(2) liters of fluid. The real numbers have no justification in the real world.

[Anonymous No.11547610]

>>11547604
>there are dozens of *book* deriving the existence of God from the ancient scriptures.
The notion of “faith” means that it is unprovable.

> If you're gonna keep dodging the question
Which one?

> calling upon your sacred scripts
If you were interested in disproving a sacred text wouldn’t be the first thing to read it?

[Anonymous No.11547649]

>>11547610
I read it, you motherfucker.
I read it all.
Nothing makes sense at all.
Since college, all you motherfuckers did was just write what you're told to write and repeat "it's how it is ask someone else".
Nobody gives proper reasoning.
Nobody explains WHY. Everyone just accepts things as they are.

Fuck you all. Fuck this shit. Math sucks.

[Anonymous No.11547655]

>>11547649
>Math sucks.
I too hate cars, planes, bridges, computers and basically every modern technology.

[Anonymous No.11547665]

>>11547649
>monkey sniffs at book, not impressed
wanna bananna?

[Anonymous No.11547749]

>>11547665
Fuck you, you fucking Christian.

[Anonymous No.11547751]

>>11547528
>Yeah, well, WHY is it the fucking definition?
do you have a better one ?

[Anonymous No.11547792]

>>11547550
>Explain to me, from bottoms up, why exactly does 0.999... != 1, without invoking your divine scriptures
All real numbers are supposed to represent points on a number line. This is all you need to accept. That's how Greeks perceived numbers - as lengths of line segments.

Integers are like marks on a ruler, this is basically a choice of scale. Closed line segments between the marks (say 1 and 3) are denoted as [1,3], you get the idea.

Fractions are also clear: for example 4/6 means divide the segment [0,1] into 6 parts of same size. The number 4/6 is the fourth mark.

But only very few points on the number line can be described as a fraction. So we need a way to describe EVERY point on the number line. Decimal expansion is the best we have come up with. This is how it works on an example:

0.999... has integer part zero. That means that the point lies somewhere in the segment [0,1].

The first decimal digit is 9. That means that the point lies in somewhere in the segment [9/10,10/10]

The second decimal digit is 9. That means that the point lies somewhere in the segment [99/100,100/100].

The third decimal digit is 9. That means that the point lies somewhere in the segment [999/1000,1000/1000].

And so on.

The only point on the number line which satisfies all of this is 1. This can be proved using high school geometry basically.

The thing is that you need to define the decimal expansion (as explained above) using CLOSED line segments [a,b] as I did, and not open segments (a,b) nor half-open segments [a,b). This is simply a technical issue, it just wouldn't work otherwise. This results in the unpleasant fact that one numbers can have two distinct decimal expansions. Ultimately it's just a consequence of the fact that the closed segments [0,1] and [1,2] share a point in their intersection.

[Anonymous No.11547795]

>>11547792
quoted wrong post, sorry

[Anonymous No.11547835]

>>11547544
>arguing with retards on the internet just so someone will talk to you
Based, have your (you)

[Anonymous No.11547876]

>>11547504
>allow the never-explained "go-to-infinity" step
Only crackpots talk about it. It beats me too why crackpots are still allowed. They are like people who urinate and defecate in public swimming pools.

[Anonymous No.11547885]

>>11547508
The real question is that why does the =/= side always sound like schizos especially in the OP

[Anonymous No.11547923]

The algebraic proof doesn't make sense to me.
When you multiply 0.99... by 10, surely, there is a place at the end of infinity which changes from a 9 to a 0. Is it even infinity anymore if you multiply it by 10?

[Anonymous No.11547956]

>>11547923
>a place at the end of infinity
Be warned never to let a constructivist hear you say such a thing. They will immediately ask you do demonstrate this "end of infinity" which you postulate. Which you obviously cannot do.

[Anonymous No.11548003]

OP is correct.
A bowling ball would never hit a pin if it was 99.999...% of the way.
In my understanding 1 and 0 is all there is in our universe.
Well then what is 2 then? You will ask. 2 is a lazy way of explaining two 1's. What about 0.50 then you pseud??? The scale is off and its fifty seperate 1's.
A 1 is the entity that allows us to exist it's more than just a number. But you must have 0 first.
0 is the first number, 1 is the last.

[Anonymous No.11548010]

>>11547956
Can you demonstrate infinity, though?

[Anonymous No.11548021]

>>11548003
Why does this make sense????

[Anonymous No.11548031]

>>11548003
>>11548021
We live in a fucking computer CONFIRMED.

[Anonymous No.11548036]

>>11548003
What about negative numbers anon?

[Anonymous No.11548052]

>>11548036
-1 and 1 represent the exact same thing.

[Anonymous No.11548058]

>>11548003
Can someone please step in and disprove this mad man. It actually makes sense and its way too obvious.

[Anonymous No.11548067]

>>11548003
>>11548052
Ok, now this is based...

[Anonymous No.11548068]

>>11548003
Only reddit believes this faggotshit.

[Anonymous No.11548085]

>>11548068
Nice counterpoint, really disproved me wrong there with that name calling.

[Anonymous No.11548089]

>>11548085
>Everything is 0 or 1 XD.
Only retards believe that.

[Anonymous No.11548095]

>>11547504
Maths student here, please stop these schizo threads
First method : you can caracterize equality this way [math](\forall\varepsilon>0,|x-y|<\varepsilon)\Leftrightarrow(x=y)[\math] (just think of it as trying to figure out 1-0.999..., which is 0.00... so 0)

Second method : Nested intervals theorem (basically what >>11547792 did)

You can also use sequences and sums, which is basically using the concept of limits.

[Anonymous No.11548098]

>>11548089
See >>11548068

[Anonymous No.11548103]

>>11548095
Fucked up the latex:
[math](\forall\varepsilon>0,|x-y|<\varepsilon)\Leftrightarrow(x=y)[/math]

[Anonymous No.11548108]

>>11548098
? Reddit and retards are the same thing.

[Anonymous No.11548117]

>>11548003
Makes sense actually.

[Anonymous No.11548119]

>>11548103
Ok I give up, basically it's saying that if two numbers are infinitely close (whatever non-zero number is greater than their distance), these two numbers are equal

[Anonymous No.11548127]

>>11548003
>>11548052
ALL WAS NONE
NOW ALL IS ONE

[Anonymous No.11548155]

>>11548068
>>11548108
NOOOOOO!!! YOU CANT JUST SOLVE THE MATHERINO!!! NOT THE CUTE NUMBERS!!!

[Anonymous No.11548181]

>>11548155
>NOOOOOO YOU CANT JUST DENY MY POPSCI MATH I MADE UP WHILE STONED AND WATCHING RICK AND MARTY!!! ITS SUPPOSE TO BE WHOLESOMERINO AND GET UPBOATS AND YOUS

[Anonymous No.11548871]

i made a satisfying proof using binomial theory.
feel free to provide the counterexample...do you have a supercomputer to fry?

[Anonymous No.11548874]

>>11548058
>>11548871
here, if you have any questions ill explain.

[Anonymous No.11548901]

>>11548003
That's just base 1 regular math you nigger

[Anonymous No.11548941]

>>11547792
Wrong. There's another point on the number line in those intervals. The point 0.999..., which is different from 1. According to your logic, it must be in [0,2], [9/10,2], [99/100,2], etc. So 0.999 = 2. This is what you onetards don't understand. It's just the principle of lexicographical ordering that 0.999! = 1

[Anonymous No.11548949]

>>11548941
What do you think the real numbers are?

[Anonymous No.11548956]

>>11548095
Math PhD here. 0.999 is not 1

[Anonymous No.11548957]

>>11548003
Your explanation is just a fancy way of saying the natural and rationals are countable. If you can explain the decimal representation of an irrational I'll be impressed.

[Anonymous No.11548971]

>>11548949
What do you think infinity is, onetard?

[Anonymous No.11548977]

>>11548941
>There's another point on the number line in those intervals. The point 0.999..., which is different from 1
prove it

[Anonymous No.11548987]

>>11548977
1-0.999...=0.000...01
Their difference is not zero qed

[Anonymous No.11549003]

>>11548987
That number does not exist, at least if you want the least upper bound axiom to hold. A number "inifnitely" close to zero, but different from it does not exist, and has been proven not to exist.

Why does /sci/ still have these threads?

[Anonymous No.11549013]

>>11549003
Whatever you say man. Your word makes things exist or not exist

[Anonymous No.11549023]

>>11548987
>0.000...01
is this number supposed to be smaller than 1/10^n for all natural numbers n ?

[Anonymous No.11549030]

>>11549013
https://en.wikipedia.org/wiki/Archimedean_property#Archimedean_property_of_the_real_numbers
You can read the proof here if you want. I'm not saying that the idea of 0.000...01 is dumb and and of itself, just that there is no good way of having a number "infinitely" close to another in the reals. You can still play around with 0.000...01, but it can't be a _real_ number.

[Anonymous No.11549122]

>>11547792

>The only number between n and something arbitrarily close to n is n
>between n and something
>between n
>between

the absolute state of 0.999... = 1 fags

[Anonymous No.11549164]

>>11547572
It's weird to think how the diagonal of a 1 by 1 square is EXACTLY sqrt(2) even though you can't write out the number. That fact alone makes me feel cozy.

[Anonymous No.11549181]

>>11549122
>>The only number between n and something arbitrarily close to n is n
that's pretty much how it works, yes

[Anonymous No.11549196]

>>11549181
>between

[Anonymous No.11549207]

>>11548871
>binomial theory

[Anonymous No.11549215]

>>11549196
yep

[Anonymous No.11549231]

>>11547549
You can easily define 0.000...1 as a function from [math]\omega+1[/math] to [math]\{0,1\}[/math].

[Anonymous No.11549256]

>>11548956
Inventor of math here .999.. =1

[Anonymous No.11549277]

>>11547520
>>11547532
>>11547545
>>11547548
>>11547549
>>11549003
>>11548977

[Anonymous No.11549285]

>>11549256
Since obviously the notion of "invention" is reserved for anything that we all learn in school.

[Anonymous No.11549426]

>>11547577
>There's a pink elephant flying around in my room
>A bunch of fairies live in my backyard
Nothing about this is contradictory or confusing or difficult to understand

[Anonymous No.11549435]

>>11548003
You cant have 0 first, because then it wouldn't exist. The only thing in our Universe is 1.

[Anonymous No.11549452]

>>11549277
>0.999... can be represented by this formula
For which x is y=0.999...?

[Anonymous No.11549453]

>>11548095
>>Maths Nazi here
>Follow orders like a good little Maths Nazi.
>Genocides Finite Universe

[Anonymous No.11549518]

>>11549452
lmao good luck getting an answer to that

[Anonymous No.11549649]

If 0,999...=1
So 0,899...=0,999...=1
So 0,889...=0,899...=0,999...=1
Fast forward
So 0,00000001234678999999999...=1
If there is no number between 0,999... and 1 so therefore they're equal, since there is no number between 0,899... and 0,999... they're also equal. If a=b and b=c, a=c.
You could push this forever and reach the conclusion that 0,00000199999... = 1.
Approximation is bad. It leads to something akin to the prisonner dilemma.
As I see it, finite and infinite decimal numbers represent different concepts and shouldn't be mixed. But 0,999... isn't equal to 1, it's a different concept alltogether and maths shouldn't include infinite concepts, 0,999... doesn't exist because it doesn't occur in nature, it's just a concept, while 1 occurs in nature.

[Anonymous No.11549665]

>>11549649
>since there is no number between 0,899... and 0,999...
What about 0.95?
retard

[Anonymous No.11549672]

>>11547520
is that because, forever, for infinity, you will be there to say "but theres another 9?"

[Anonymous No.11549678]

>>11549649
0.9...=1
0.89...=0.9
thats how rounding works

[Anonymous No.11549757]

>>11549207
whatever dickhead im still right. my proof is flawless.

[Anonymous No.11549791]

>>11549678
For cashier level intelligences.

[Anonymous No.11549793]

>>11549791
I can help whoever's next please

[Anonymous No.11550133]

>>11547504
>Who the fuck cares about the 0.00000.....0001?
I am laughing but I feel your pain. If it were there I'd be incensed as well. But it's just not there man. Imagine subtracting .999 from 1 but starting on the left. You would have 1.0 - .9 and get a .1 but .1 - .09 = .01. Any one you may have presumed to exist had already been subtracted. Which is why we don't start on the left.

[Anonymous No.11550136]

>>11547515
Based. Never stop

[Anonymous No.11550160]

>>11549665
kek

[Anonymous No.11550161]

>>11548971
An unbounded quantity that is greater than every real number.

[Anonymous No.11550201]

>>11547515
>In it's origin, the inability to understand infinity and eternity is 100% Judaic in thought/philosophy. In contrast, the non-Jewish man; the Pagan man, at least the /European/ Pagan man, never had any problem with infinity and eternity.
Already contradicting yourself by excluding the overwhelming majority of Christian Europeans. Most major Christian sects were founded in Europe. Keep trying hard Schlomo at playing both sides, you and your polytheistic scum will get wrecked soon

[Anonymous No.11550305]

>>11549452
It isn't. 0.999.... Is ill-defined.

[Anonymous No.11550340]

>>11547504
0.999... = 1 even in the surreals.
Maybe try reading something about surreal analysis: https://arxiv.org/abs/1307.7392..

[Anonymous No.11550343]

>>11549277
https://www.wolframalpha.com/input/?i=0.999......

[Anonymous No.11550347]

>>11550305
Nah, it's perfectly well-defined. It's [math]\sum_{n=1}^\infty \frac{9}{10^n}[/math], which is 1.

[Anonymous No.11550394]

>>11549452
The function itself is 0.999

[Anonymous No.11550398]

>>11550201
>polytheistic
lol jews literally invented monotheism you dumb goy

[Anonymous No.11550462]

>>11550394
lrn2write

[A No.11550489]

Oh a shit post bait thread? Let me start another one sec

[Anonymous No.11550586]

How tf did you pass third grade?I remember my hs class freaking but this is Ohio. Are you retarded? Is there at least some sort of ability to function in the real world for people who believe in ...01? Like if I asked you to divide 1/3 and then multiply by 3 would your fucking head explode? Or would you be able to do it and yet still deny it like fucking Patrick the starfish?

>>11548941
This is a funny and retarded idea. .9 and 1 are different points right? What if you added .1 to .9? Yup that's 1. And that's exactly what .999... is.

It's very clear anyone who thinks 1!=.999... should not be here. Just like they shouldn't have bothered letting you take anything past geometry. You're holding everyone else back without even realizing how fucking elementary this idea is. Like wtf does your brain even do to get you to this point? .999... doesn't ever approach 1 with an eternal damned ...1 always sneaking around. It already is 1. We might as well just teach you this >>11548003 so we don't blow your tiny brain up. It isn't just some shortcut mathematicians have used to make things easier. If I were to decompose 1 into a set of numbers each accounting for every decimal place between 0 and infinity, I would have .9, .09, .009, etc. If I added them all together I would get .999... or I could call it 1 because it is the same. It is essentially a box representing 1 that has been completely filled. But the only actual reason I would need to write 1 is if I were planning to write a number larger than one such as 1.0001

[Anonymous No.11550593]

0.999 is an approximation of 1

[Anonymous No.11550622]

>>11550593
lrn2write

[Anonymous No.11550667]

>>11547649
cope harder, mathlet

[Anonymous No.11550756]

>>11547504
Exactly
Limits are bullshit
Equivalence classes of the differences of Cauchy sequences “defined” by their “limit” at 0 are also bullshit

[Anonymous No.11550759]

>>11550756
seething retard

[Anonymous No.11550833]

>>11547504
0! = 1

0.n! = 1

What's so hard about this for others to get?

The whole point of calculus is to exhaustively grind into dust the arguments or inputs of 'but what about my special interpretation?'

[math]xy log z log e = n log n[/math]

How many more arguments would a mathematician ever want to work on if not some quotient and remainder of other peoples observations?

Or don't any of you know of the Vagus conjecture that proves all of this geometrically?

[Anonymous No.11550850]

>>11550394
that's strange I've always thought 0.999... is a number

[Anonymous No.11551044]

>>11550305
Ill defined by you.

>>11550394
Then the function never reaching 1 is as irrelevant as the function never reaching 0.999...

[Anonymous No.11551237]

>>11547604
but you dont have two rocks. two rocks didnt exist before man conceived the number system to define them as two rocks. furthermore you may hold two rocks and say "i have two rocks" but there are an infinite amount of rocks in the universe. you are the observer, observing two rocks and that number is only true from your perspective.

[Anonymous No.11551282]

>>11548957

The issue here isn't whether the number is irrational or not, the issue here is whether the program that produces the number can terminate in finite time. Have you ever calculated the square root of 2 by hand without using newton's method? it's just like long division, that is, you are repeatedly executing a finite number of steps. The problem is that the program doesn't terminate in finite time- which leads us to the same dilemma many have with the equality relation between 0.999... and 1. 0.999... requires a finite program to calculate, but the program does not terminate in finite time. If it doesn't terminate in finite time, how can you evaluate the equality relation on it?

[Anonymous No.11551353]

>>11551282
>The issue here isn't whether the number is irrational or not, the issue here is whether the program that produces the number can terminate in finite time.
There are programs that produce 1 in finite time and programs that don't produce 1 in finite time. It has no relevance to whether 1 exists.

>Have you ever calculated the square root of 2 by hand without using newton's method?
Every digit of 0.999.. is known, so I don't see what this has to do with anything.

[Anonymous No.11551391]

>>11551353

Captain obtuse returns.

[Anonymous No.11551400]

>>11551391
Not an argument, try again.

[Anonymous No.11551429]

>>11551282
and why would you think that everything needs to be computed or evaluated by a program which terminates in a finite time:

"for all natural number n we have n^2 ≥ n"

this is a true statement, but how would you know ?? the program which verifies this for all numbers will not terminate in finite time.

[Anonymous No.11551445]

>>11547649
>nothing makes sense
Have you considered that you're just stupid anon? Most people here ended up proving it for themselves. Just because it's not the most intuitive thing doesn't mean it isn't a natural consequence of the definition

[Anonymous No.11551454]

>>11548003
>haha, I gotcha, extending the additive and multiplicative identities to rational and integer expansions.
You almost have a point if we're talking topology, where (0, 2) and (0, 1) as subsets of reals with the inherited topology behave in the exact same way, but in general your ideas don't hold water

[Anonymous No.11551482]

>>11551429
>but how would you know??

Upper bounds my friend. Why do you fear finitude?

What is wrong with saying, "It's probably true but we can only verify it up to whatever can be computed."?

There seems to be a divide in mathematics not dissimilar to the divide between intelligent design/creationists and non-creationists. Creationists are uncomfortable with the idea that they evolved from something less than them, that there was an evolutionary process that needed to take place for them to exist, that they came from something less than perfect. Scientists are not uncomfortable with this idea, and thus the theory of evolution does not bother them- it is simply the best explanation for the data.

Likewise, in mathematics- especially set theorists, seem to believe that sets of numbers just "exist" independent of the program that created them, and some often deny that the program is even necessary. They will claim that the natural numbers is not created by the successor function, but that it exists independent of this function. Mathematicians who ascribe to the computational viewpoint are thus more like scientists who "believe" in the theory of evolution. By slowly accumulating data, they build a theory that supports and is consistent with their observations. Likewise, from the computational perspective, "sets" of numbers do not just exist independent of a function, but are produced by a function and is specific to the instruction set of those functions.

[Anonymous No.11551490]

>>11551482
...you're trying to talk about constructivism, which is well studied and accepts analysis unlike you lmao.
Study any sort of type theory or computable analysis and you'll see the rhetoric you peddle doesn't hold water.
But we all know you're the anon from 2-3 days ago who got BTFO'd because they understood nothing about analysis, constructive mathematics and computability / complexity.

[Anonymous No.11551506]

[Anonymous No.11551520]

>>11551482
>What is wrong with saying, "It's probably true but we can only verify it up to whatever can be computed."?

Q: is x+1 > x true?
A: by basic laws of arithmetics, this inequality is equivalent to 1 > 0, which we know is true. therefore so is the original one.

Q: is x+1 > x true ?
A: well, it's probably true, but we're not sure. it's been verified only for a few values of x. we'll never be sure.

one is clever way of doing mathematics. one is retarded way of doing mathematics.

[Anonymous No.11551536]

>>11551490

You do understand that I give zero weight to your comment because it essentially boils down to "nuh uh you're dumb dumb" right? You haven't refuted any of the individual claims I made in my comment. You are just repeating the same claim, over and over and over again, that because you (falsely) assume I haven't read the *required* texts to understand the viewpoint of a subject I am allegedly advocating for, that I must not understand the words that I am using. This is a very boring appeal to authority, but also because you have no actual counter argument you are instead trying to throw my emotions off balance by being condescending. This is very petty misdirection. Have you ever dealt with a narcissistic woman before? Do you know how they deal with being wrong? They attack your emotions and avoid the substance of the actual claim. It is sad to see you do this all while claiming to allegedly defend institutions of higher learning.

[Anonymous No.11551542]

>>11547504
Is everyone on this board retarded?

[Anonymous No.11551562]

>>11551520

so then

1-0.1^(x) < 1-0.1^(x+n) < 1

[Anonymous No.11551592]

>>11551490
>the rhetoric you peddle doesn't hold water

Literally the whole time I've been saying that equality between non-zero non-terminating sequences (reals) and terminating sequences (terminating reals) doesn't hold but inequality does. This makes sense because if a sequence hasn't terminated you don't know the value of it until it does.

From wikipedia:

>The computable real numbers form a real closed field (Weihrauch 2000, p. 180). The equality relation on computable real numbers is not computable, but for unequal computable real numbers the order relation is computable.

Literally the same exact fucking thing I was saying. You don't need to read a textbook to come to this conclusion, you need the ability to think logically. Accepting dogma != logical thought.

[Anonymous No.11551611]

>>11551592
0.999... is computable though. It's funny how you quote shit that you don't even understand while complaining about "accepting dogma."

[Anonymous No.11551635]

>>11551611
>The equality relation on computable real numbers is not computable

Read it again, slowly.

[Anonymous No.11551649]

>>11551611
>>11551635

Here I'll help you out by breaking down the statement into smaller pieces to make it easier to read

>the equality relation
>on computable real numbers
>is not computable

Did that help?

[Anonymous No.11551677]

>>11551635
>IT'S NOT COMPUTABLE REEEE
But it's provable. See >>11547548

[Anonymous No.11551690]

>>11551677
>provable but not computable

I thought proofs were computations and vice-versa mr. constructivist?

[Anonymous No.11551715]

>>11547504
Stop being retarded.

[Anonymous No.11551721]

>>11551690
Who?

[Anonymous No.11551740]

>>11551721
>This isn't an argument!
>Yes it is.
>No it isn't you're just contradicting me!
>No I'm not.

His next reply is going to be:
>Who are you quoting?

Yawn.

[Anonymous No.11551772]

>>11551740
I have no clue what you're talking about.