/sci/ - Science & Math » Thread #12232230

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Anonymous Wed 14 Oct 21:55:57 2020 No.12232230 View Reply Original Report

Quoted By: >>12232246 >>12232263 >>12232413 >>12232822 >>12232848 >>12233360 >>12233482 >>12233511 >>12233642

0.99999... != 1
lemme explain. suppose you have 1 infinitely large program, so an infinite number of lines of code. you are doing a file transfer from 1 infinitely large storage to another but 1 conditional statement the program relies on fails to transfer so you have 0.99999... of the program transferred. the program therefore does not operate.
0.99999... != 1
qed

Anonymous

Anonymous Wed 14 Oct 2020 21:59:56 No.12232246 Report

Quoted By: >>12232254

>>12232230
But 0.999... of the program is the whole program.

Anonymous

Anonymous Wed 14 Oct 2020 22:01:36 No.12232254 Report

Quoted By: >>12232273

>>12232246
except it's missing 0.0000...1 of it and doesn't run.

Anonymous

Anonymous Wed 14 Oct 2020 22:03:02 No.12232263 Report

Quoted By:

>>12232230
>thinking ?-1 is a meaningful statement

infinity is bigger than you think

Anonymous

Anonymous Wed 14 Oct 2020 22:05:53 No.12232273 Report

Quoted By: >>12232291

>>12232254
>0.0000...1
No such thing

Anonymous

Anonymous Wed 14 Oct 2020 22:08:01 No.12232280 Report

Quoted By: >>12232291

? - 1 = ?
So you have equal amounts of code in both programs. Into the trash your proof goes.

Anonymous

Anonymous Wed 14 Oct 2020 22:11:54 No.12232291 Report

Quoted By: >>12232300 >>12232348 >>12232756

>>12232273
yes there is.
1-0.99999... = 0.0000...1

>>12232280
clearly that is wrong as this thought experiment shows. math has been wrong for all these years until my proof by shitpost on this laotian finger painting forum.

Anonymous

Anonymous Wed 14 Oct 2020 22:14:28 No.12232300 Report

Quoted By: >>12232337

>>12232291
>yes there is.
>1-0.99999... = 0.0000...1
Wrong.

Anonymous

Anonymous Wed 14 Oct 2020 22:21:38 No.12232337 Report

Quoted By: >>12232346

>>12232300
nope, infinitely large program missing 1 line of code is that.

Anonymous

Anonymous Wed 14 Oct 2020 22:22:33 No.12232346 Report

Quoted By:

>>12232337
Wrong

Anonymous

Anonymous Wed 14 Oct 2020 22:22:42 No.12232348 Report

Quoted By: >>12232364 >>12232566

>>12232291
Two proofs 0.0000...1 = 0:

Via Cauchy sequences:

0.000...1 = (0.1, 0.01, 0.001,...) = lim as n-> inf of 1/10^n = 0

Via Dedekind cuts:

Assume to contradiction that x is a rational number such that

0 < x < 0.000...1

0.000...1 is less than any finite string of 0s followed by a 1 so for any natural number n

0 < x < 0.000...1 < 1/10^n

x < 1/10^n

10^n < 1/x

n < log(1/x)

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

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

This is a contradiction, so x does not exist and 0.000...1 = 0.

Anonymous

Anonymous Wed 14 Oct 2020 22:27:03 No.12232364 Report

Quoted By: >>12232371 >>12232388

>>12232348
>lim as n-> inf of 1/10^n = 0
that is a limit so it approaches 0 but isn't true 0.

>Assume to contradiction that x is a rational number such that
>0 < x < 0.000...1
this x dne to begin with. 0.000...1 is the smallest possible number.

Anonymous

Anonymous Wed 14 Oct 2020 22:27:37 No.12232367 Report

Quoted By:

IT IS 1 BY DEFINITION YOU IMBECILES! THERE IS NO 0.9999...

Anonymous

Anonymous Wed 14 Oct 2020 22:28:04 No.12232371 Report

Quoted By:

>>12232364
*before 0.

Anonymous

Anonymous Wed 14 Oct 2020 22:34:04 No.12232388 Report

Quoted By:

>>12232364
>that is a limit so it approaches 0 but isn't true 0.
No, the limit is 0. What isn't 0 is 1/10^n for any natural number n. Welcome to elementary school math.

>this x dne to begin with.
Then 0.001... = 0 by construction of the reals.

>0.000...1 is the smallest possible number.
Yes, 0.

Anonymous

Anonymous Wed 14 Oct 2020 22:40:11 No.12232413 Report

Quoted By:

>>12232230
Idk man I ate .999.. bagels today

Anonymous

Anonymous Wed 14 Oct 2020 23:18:08 No.12232566 Report

Quoted By: >>12232597 >>12232761 >>12234363 >>12234432

>>12232348
>Via Cauchy sequences
All this shows is that 000...1 approaches 0, not that it is actually equal to 0. You may say that it is *effectively* equal to 0, but when talking with exact precision as mathematicians should, 0.000...1 merely rounds down to 0 in physical circumstances. It does not actually exactly equal 0.
>Via Dedekind cuts
There is no fraction between 0.000...1 and 0. Sure. 0.000...1 is still not equal to 0, onefag. Doesn't prove anything.

Now to thoroughly BTFO you drooling retard onefags, I'll provide two proofs that 0.999... does not equal 1.

Limiting behavior
$0.9<1\\0.99<1\\0.999<1\\\ldots$ Now by examining the behavior of this sequence as it extends to infinity, we see a uniform pattern here. That they are NEVER equal, and that 0.999... is ALWAYS less than 1. Hence, $0.\overline{9}\neq1$ .

Proof by contradiction
$1-0.\overline{6}=0.\overline{4}\\0.\overline{9}-0.\overline{6}=0.\overline{3}\\0.\overline{4}\neq0.\overline{3}\\0.\overline{9}\neq1$

Anonymous

Anonymous Wed 14 Oct 2020 23:25:03 No.12232586 Report

Quoted By: >>12232590 >>12232601 >>12232604 >>12232686 >>12232771 >>12232840

If 0.999...99 = 1, then what's stopping 0.999...98 = 0.999...99?
You may as well just say 1 = 0 and be done with it.

Anonymous

Anonymous Wed 14 Oct 2020 23:26:05 No.12232590 Report

Quoted By:

>>12232586
>0.999...98 = 0.999...98?
In truth, I was the retard.

Anonymous

Anonymous Wed 14 Oct 2020 23:27:38 No.12232597 Report

Quoted By:

>>12232566
>All this shows is that 000...1 approaches 0
0.000...1 is not a function, it doesn't "approach" anything.

>not that it is actually equal to 0
It shows that it's exactly equal to 0, look up the construction of the reals via Cauchy sequences. Do you have an actual argument?

>There is no fraction between 0.000...1 and 0.
Then they are equal. Thanks for playing.

>Now by examining the behavior of this sequence as it extends to infinity, we see a uniform pattern here.
Yes, a pattern for finite amounts of 9s, not a proof of anything. This tells us nothing about infinite 9s. And I can easily show that 0.999... is not less than 1 by a proof similar to the one you failed to counter.

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

Anonymous Wed 14 Oct 2020 23:29:12 No.12232601 Report

Quoted By:

>>12232586
>If 0.999...99 = 1,
0.999...99 is not a thing at all, and thus doesn't equal anything. Only 0.999... is.

Anonymous

Anonymous Wed 14 Oct 2020 23:30:15 No.12232604 Report

Quoted By:

>>12232586
>You may as well just say 1 = 0 and be done with it.
there is no end to .999...
you cant flip the "last 9" to an eight
even if you could, you couldnt ever remove infinitely many 9's before it to reach 0

Anonymous

Anonymous Wed 14 Oct 2020 23:52:21 No.12232686 Report

Quoted By:

>>12232586
>You may as well just say 1 = 0 and be done with it.
that's true though, in mod 1

Anonymous

Anonymous Thu 15 Oct 2020 00:13:07 No.12232756 Report

Quoted By:

>>12232291
>1-0.99999... = 0.0000...1
1-1=0

Anonymous

Anonymous Thu 15 Oct 2020 00:14:14 No.12232761 Report

Quoted By:

>>12232566
>let's pretend finite is infinite

Anonymous

Anonymous Thu 15 Oct 2020 00:17:07 No.12232771 Report

Quoted By:

>>12232586
>0.999...99 = 1, then what's stopping 0.999...98 = 0.999...99
nothing, anything after the ellipsis is just n*10^-inf=0
0.999...98 = 0.999...99 = 0.9... = 1

Anonymous

Anonymous Thu 15 Oct 2020 00:33:24 No.12232822 Report

Quoted By:

>>12232230
It’s literally close enough, don’t be such a fucking sperg about it

Anonymous

Anonymous Thu 15 Oct 2020 00:38:36 No.12232840 Report

Quoted By:

>>12232586
>0.999...98 = 0.999...99

Because those are nonsensical notations that you made up. Show one example of any one ever using repeating digit notation in that way besides you.

Anonymous

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Anonymous Thu 15 Oct 2020 00:40:44 No.12232848 Report

Quoted By: >>12233501

>>12232230
Fuck you, stop shitting up the post with mathematical illiteracy and take a calc 2 course.

Anonymous

Anonymous Thu 15 Oct 2020 03:51:35 No.12233360 Report

Quoted By: >>12233421 >>12233429

>>12232230
This is a traversal problem like Hercules chasing the tortoise.

Anonymous

Anonymous Thu 15 Oct 2020 04:22:50 No.12233421 Report

Quoted By:

>>12233360
You're an idiot.

Anonymous

Anonymous Thu 15 Oct 2020 04:25:33 No.12233429 Report

Quoted By:

>>12233360
it was Achilles, retard

Anonymous

Anonymous Thu 15 Oct 2020 04:51:52 No.12233482 Report

Quoted By:

>>12232230
No, the cardinality of the string of nines is equal to the infinite number of nines.
.99...=1
>x=.99...
>10x=9.99...
>10x-x=9.99...-.99...
>9x=9
>x=1

Anonymous

Anonymous Thu 15 Oct 2020 04:59:12 No.12233501 Report

Quoted By: >>12233652

>>12232848
>let me define 0 to be 1,therefore 0 = 1!!!! 1!1!!
Fuck off

Anonymous

Anonymous Thu 15 Oct 2020 05:01:10 No.12233504 Report

Quoted By: >>12233657 >>12233945

The very fact that this is even an issue, and furthermore there are so many 'proofs' that either support or debunk this, means to me that our implementation of mathematics is *broken*.

Anonymous

Anonymous Thu 15 Oct 2020 05:03:58 No.12233511 Report

Quoted By:

>>12232230
Your face = your butt
lemme explain. suppose you have 1 infinitely gay face, so an infinite homosexual faggotry. you are doing a shit cum bomb from 1 infinitely gay face to another but 1 giant poopy asshole and the face relies on poop to transfer so you have 100% of the poop blasted onto the butt, the butt then has to be the face.
your face is your butt and your butt is your face
qed.

Anonymous

Anonymous Thu 15 Oct 2020 05:52:09 No.12233642 Report

Quoted By:

>>12232230
This explains the situation. Talk given in layman terms by a guy with a degree in Pure Mathematics, and a doctorate in Algebraic Number Theory
https://vimeo.com/24014769
Thank me later.

Anonymous

Anonymous Thu 15 Oct 2020 05:58:25 No.12233652 Report

Quoted By:

>>12233501
0.9...=0!!!

Anonymous

Anonymous Thu 15 Oct 2020 06:00:53 No.12233657 Report

Quoted By:

>>12233504
>means to me that our implementation of mathematics is *broken*.
it actually means that the typical human is incredibly poorly suited for thinking, as your comment shows

Anonymous

Anonymous Thu 15 Oct 2020 08:56:00 No.12233945 Report

Quoted By:

>>12233504
>The very fact that this is even an issue
it's not an issue

Anonymous

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Anonymous Thu 15 Oct 2020 12:16:23 No.12234349 Report

Quoted By: >>12235141 >>12235160 >>12235376 >>12235583

btfo

Anonymous

Anonymous Thu 15 Oct 2020 12:23:54 No.12234363 Report

Quoted By:

>>12232566
Your proof is shit.
You have to show that your pattern is true for any rational number, but you have instead just assumed that it's true until infinity.
You can't assume your conclusion.

Anonymous

Anonymous Thu 15 Oct 2020 13:00:27 No.12234432 Report

Quoted By:

>>12232566
>Now by examining the behavior of this sequence as it extends to infinity, we see a uniform pattern here.
what "uniform pattern" are you talking about? what is the exact relation between 0.999... and the lines 0.9, 0.99, 0.999,... ? can you prove that this relation preserves strict inequalities?

Anonymous

Anonymous Thu 15 Oct 2020 17:22:42 No.12235141 Report

Quoted By: >>12235160

>>12234349
Argument 3 is nonsensical.

“...” is used to denote repetends in decimals not for infinitely extended operations. The “white space” you put in (2) doesn’t mean anything. You just bastardized the symbol for something it wasn’t meant for, did a nonsensical thing, and got a nonsensical result. It has nothing to do with whether 9.999... - 0.999... = 9 because it’s clear that what it’s referring to, that it’s a form of recurring decimal rotation. What you’re doing with the 1-1+1-1+1-1+... is your made own made up bastardization of recurring decimal notation.

Anonymous

Anonymous Thu 15 Oct 2020 17:31:29 No.12235160 Report

Quoted By: >>12235355

>>12235141
>>12234349

But let’s say for sake of argument that you can use the symbol that way. “...”

The pattern is:
1 - 1 =0
1 - 1 + 1 - 1 = 0
1 - 1 + 1 - 1 + 1 - 1 = 0

It just always 0’s out. If you added expression (1) and (2) together you’d just get 2x = 0
X = 0

Wow how interesting.

Anonymous

Anonymous Thu 15 Oct 2020 18:16:20 No.12235355 Report

Quoted By: >>12235373

>>12235160
9.9 - 0.9 = 9.0
9.99 - 0.99 = 9.0
9.999 - 0.999 = 9.0
9.9999 - 0.9999 = 9.0
9.99999 - 0.99999 = 9.0
...
9.999... - 0.999... = 9.0

These are all the same:
$9.99... = 9.999... = 9.\overline{9}$

X = 0.333...
X * 10 = 3.333...
10x - 1x = 3.333... - 0.333...
9x = 3.0
X = 3/9
X = 1/3

0.3 - 0.3 = 0
3.3 - 0.3 = 3.0
3.33 - 0.33 = 3.0
3.333 - 0.333 = 3.0
3.3333 - 0.3333 = 3.0
3.33333 - 0.33333 = 3.0
...
3.333... - 0.333... = 3

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

Anonymous

Anonymous Thu 15 Oct 2020 18:21:18 No.12235373 Report

Quoted By:

>>12235355
It’s not “absurd”... it’s not “weird”...

.999... and 1 are just two different notations of the same value.

Anonymous

Anonymous Thu 15 Oct 2020 18:21:51 No.12235376 Report

Quoted By:

>>12234349
>1-1+1-1+1-1+
any proof dependent on the order of adding is bs

Anonymous

Anonymous Thu 15 Oct 2020 19:13:30 No.12235583 Report

Quoted By:

>>12234349
>cant into Divergent series
fucking undergrads

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