/sci/ - Science & Math » Thread #11546563

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Will ANY OF YOU SHUT THE FUCK UP ABOUT 0.999...?

Anonymous Thu 09 Apr 02:21:18 2020 No.11546563 View Reply Original Report

Quoted By: >>11546565 >>11546569 >>11546718 >>11547349

It should be considered spam. Like it's worse than COVID-19, IQ and Job threads. They bring in something new to the table, at least more than 0.999...threads

Anonymous

Anonymous Thu 09 Apr 2020 02:22:16 No.11546565 Report

Quoted By:

>>11546563
IQ threads certainly don't bring anything new to the table.

Anonymous

Anonymous Thu 09 Apr 2020 02:23:18 No.11546569 Report

Quoted By:

>>11546563
That image reeks of NPC
>public dialog
Lol, as if most people knew how to even write

Anonymous

Anonymous Thu 09 Apr 2020 03:25:41 No.11546718 Report

Quoted By: >>11547462 >>11547682

>>11546563
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

Anonymous Thu 09 Apr 2020 03:35:31 No.11546742 Report

Quoted By:

Social distancing insanity has set in. The world will inevitably descend into madness as we all shitpost for 18 hours of the day.

Anonymous

Anonymous Thu 09 Apr 2020 05:48:29 No.11547013 Report

Quoted By:

>covid tourist only just realises this board is fucking garbage

lol took you long enough

Anonymous

Anonymous Thu 09 Apr 2020 09:47:54 No.11547349 Report

Quoted By:

>>11546563
you have forgotten to include your own take on 0.999... = 1

Anonymous

Anonymous Thu 09 Apr 2020 11:26:13 No.11547462 Report

Quoted By: >>11547471 >>11547478

>>11546718
>that x is a rational number
Why would you do that?
The number between 0.999... and 1 might not be rational at all!

In the end all you did was prove that it isn't rational, not that it doesn't exist. In fact it is a perfectly reasonable number, just not rational or real.

Anonymous

Anonymous Thu 09 Apr 2020 11:33:26 No.11547471 Report

Quoted By: >>11547495

>>11547462
first of all, x can clearly be assumed rational, because if there exists a real number betwen a and b, then there exists a rational number between a and b. that's super easy to prove from the archimedean property.

second of all, x being rational number is not even used in the proof. replace the word "rational" with "real" and it works just fine.

third of all:
>In fact it is a perfectly reasonable number, just not rational or real.
so now we're talking about hyperreal numbers or what ?

Anonymous

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Anonymous Thu 09 Apr 2020 11:34:25 No.11547472 Report

Quoted By:

Anonymous

Anonymous Thu 09 Apr 2020 11:38:35 No.11547478 Report

Quoted By: >>11547506

>>11547462
>Why would you do that?
Look up the construction of real numbers by Dedekind cuts.

>In the end all you did was prove that it isn't rational, not that it doesn't exist.
Incorrect.

Anonymous

Anonymous Thu 09 Apr 2020 11:39:46 No.11547480 Report

Quoted By:

one of internet's oldest trolls and you spergs can't figure it out

Anonymous

Anonymous Thu 09 Apr 2020 11:51:51 No.11547495 Report

Quoted By: >>11547509 >>11547513

>>11547471
>so now we're talking about hyperreal numbers or what ?
The idea of defining numbers by specifying them to be “between” two sets is based on an extension to dedekin cuts, by Conway. The term surreal number was coined by Knuth.

> because if there exists a real number betwen a and b, then there exists a rational number between a and b
You are supposing a theory of real numbers for that.

Anonymous

Anonymous Thu 09 Apr 2020 11:59:15 No.11547506 Report

Quoted By: >>11547513 >>11547526

>>11547478
>Incorrect
Since it exists in some meaningful sense, this statement is incorrect.

> because if there exists a real number betwen a and b, then there exists a rational number between a and b
Assuming he numbers you want to define by dedekin cuts is rational seems “odd”.

Anonymous

Anonymous Thu 09 Apr 2020 12:00:16 No.11547509 Report

Quoted By: >>11547516

>>11547495
>The idea of defining numbers by specifying them to be “between” two sets is based on an extension to dedekin cuts, by Conway. The term surreal number was coined by Knuth.
So?

>You are supposing a theory of real numbers for that.
A theory of real numbers exists.

Anonymous

Anonymous Thu 09 Apr 2020 12:01:11 No.11547513 Report

Quoted By: >>11547516

>>11547495
>>11547506
nobody gives a shit about surreal or hyperreal numbers anon

Anonymous

Anonymous Thu 09 Apr 2020 12:02:10 No.11547516 Report

Quoted By: >>11547529 >>11547530

>>11547509
>A theory of real numbers exists.
If you assume that to be given your entire post is pointless.

>>11547513
And?

Anonymous

Anonymous Thu 09 Apr 2020 12:05:53 No.11547526 Report

Quoted By: >>11547556

>>11547506
>Since it exists in some meaningful sense, this statement is incorrect.
It doesn't exist according to standard axiomatic definitions.

>Assuming he numbers you want to define by dedekin cuts is rational seems “odd”.
I didn't define x by Dedekind cuts, I simply showed that 0.999... is the same Dedekind cut as 1 since there are no rational numbers less than which are not less than 0.999...

Anonymous

Anonymous Thu 09 Apr 2020 12:06:56 No.11547529 Report

Quoted By: >>11547556

>>11547516
>If you assume that to be given your entire post is pointless.
How so?

Anonymous

Anonymous Thu 09 Apr 2020 12:07:14 No.11547530 Report

Quoted By: >>11547556

>>11547516
I have no idea what point are you trying to make

Anonymous

Anonymous Thu 09 Apr 2020 12:15:29 No.11547556 Report

Quoted By: >>11547574 >>11547613

>>11547526
>It doesn't exist according to standard axiomatic definitions.
Of the real numbers, yes.

> I didn't define x by Dedekind cuts, I simply showed that 0.999... is the same Dedekind cut as 1 since there are no rational numbers less than which are not less than 0.999...
That is basically just a different way of saying the same thing.
If you start from dedekin cuts, and you assume x to be a number it has to be a dedekin cut, if in the end it wasn’t a dedekin cut, it wasn’t a number.

>>11547529
Because if Anybody knew a rigorous definition of he reals he wouldn’t say that 1 isn’t 0.99...

>>11547530
What point are you trying to make?

Anonymous

Anonymous Thu 09 Apr 2020 12:21:33 No.11547574 Report

Quoted By: >>11547600

>>11547556
you don't need to know about cauchy sequences or dedekind cuts to intuitively accept that reals are densely ordered and that rationals are dense in R

Anonymous

Anonymous Thu 09 Apr 2020 12:28:49 No.11547600 Report

Quoted By: >>11547618 >>11547637

>>11547574
If you accept that you can hardly deny that 1 isn’t 0.99...

Anonymous

Anonymous Thu 09 Apr 2020 12:36:09 No.11547613 Report

Quoted By: >>11547616

>>11547556
>Of the real numbers, yes.
So x doesn't exist.

>That is basically just a different way of saying the same thing.
Then why is it odd?

>Because if Anybody knew a rigorous definition of he reals he wouldn’t say that 1 isn’t 0.99...
If anyone knew the rigorous definition of the reals they should be able to come up with my proofs, yes.

Anonymous

Anonymous Thu 09 Apr 2020 12:38:06 No.11547616 Report

Quoted By: >>11547623

>>11547613
>So x doesn't exist.
There are more numbers than just the reals..

> Then why is it odd?
Unrelated.

> If anyone knew the rigorous definition of the reals they should be able to come up with my proofs, yes.
And thus wouldn’t disagree with your conclusion.

Anonymous

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Anonymous Thu 09 Apr 2020 12:38:29 No.11547618 Report

Quoted By: >>11547633

>>11547600
>if you accept the premises then you accept the conclusion
>therefore the argument is unnecessary
You realize that this is true of all logical arguments, right? The conclusion is just a tautology with the premise.

Anonymous

Anonymous Thu 09 Apr 2020 12:41:25 No.11547623 Report

Quoted By: >>11547633

>>11547616
>There are more numbers than just the reals..
Saying there are numbers outside of the reals is very different from saying there are numbers that violate the standard axiomatic definition of the reals, making their construction impossible.

>Unrelated.
?

>And thus wouldn’t disagree with your conclusion.
The same is true of every sound valid argument.

Anonymous

Anonymous Thu 09 Apr 2020 12:45:13 No.11547633 Report

Quoted By:

>>11547618
>You realize that this is true of all logical arguments, right? The conclusion is just a tautology with the premise.
Obviously. I didn’t say he was fundamentally wrong, just unconvincing.

>>11547623
> Saying there are numbers outside of the reals is very different from saying there are numbers that violate the standard axiomatic definition of the reals
You can’t violate a definition.
If you mean there are numbers which doesn’t fit the definition of the reals, there obviously are.

>?
?

> The same is true of every sound valid argument.
It’s general validity I didn’t dispute.

Anonymous

Anonymous Thu 09 Apr 2020 12:48:04 No.11547637 Report

Quoted By: >>11547642

>>11547600
>If you accept that you can hardly deny that 1 isn’t 0.99...
are you fucking serious ?

Anonymous

Anonymous Thu 09 Apr 2020 12:49:47 No.11547642 Report

Quoted By: >>11547653

>>11547637
I think so...

Anonymous

Anonymous Thu 09 Apr 2020 12:54:05 No.11547653 Report

Quoted By: >>11547659

>>11547642
if you accept that reals are densely ordered, then 0.999... != 1 if and only if there exists a real number x: 0.999... < x < 1. this is impossible, because it would imply that natural numbers are bounded.

Anonymous

Anonymous Thu 09 Apr 2020 12:55:59 No.11547659 Report

Quoted By:

>>11547653
Oh, I read through the sentence should be is not isn’t

Anonymous

Anonymous Thu 09 Apr 2020 13:01:36 No.11547682 Report

Quoted By:

>>11546718
shit proof written by a pseudo

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