/sci/ - Science & Math

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Let's instead ask why brainlets refuse to accept the infinite binary string diagonal contradiction.

>>11749752
Maybe I would ask them to convert the decimal to fraction. There are very simple methods taught in high school that don't even need the usual algebraic manipulations (these are simple too but maybe not so much for the idiot).
Like pic related

>>11749932

Whose the fucking brainlet now? Converting the decimal to a fraction uses the same assumption as converting .999... to 1.

That is the fallacy of circumlocution.

>>11749845
How do you make Cantor's proof work with binary expansions?
With decimal expansions, you always choose some number other than 9 so you don't get all nines after some point.
Is there a way to salvage the proof with binary expansions?

>>11749964
How does it not work in binary?

>>11749994
Here's a cheeky blogpost about it (april fool's joke, but the flaw he points out is legit)
https://medium.com/@VitalikButerin/cantor-was-wrong-debunking-the-infinite-set-hierarchy-e9ba5015102
Essentially using the diagonal construction you will get a string that's not in the list, but the number the string represents could still be in the list because binary expansions are not unique:
0.1111... = 1

>>11749951
So algebra is broken?

>>11750015
Just use binary sequences instead of binary expansions then.

>>11749752
lol retard, different numbers are not equal by virtue of having different values. I can believe someone this stupid exists.

>>11750023
ok but then how do you construct a bijection between binary sequences to the the reals?
Seems like a nontrivial task (there are obvious methods with Cantor-Bernstein-Schroder but do you have a simpler way?).

>>11750015
But there's no index for 0.111..., so it can't be in the list.

>>11750072
What list? What does that have to do with anything?

>>11750084
>you will get a string that's not in the list, but the number the string represents could still be in the list

>>11750095
Right, and what are you trying to say here?

>>11750099
You asked "what list?" It's the list you wrote about in the comment I replied to. What part of this is confusing?

>>11750106
I don't understand what you were trying to say with the comment
>But there's no index for 0.111..., so it can't be in the list.
Of course there isn't, that's what I said. The string 0.11... could not be on the list, but the number it represents could be in the list. So applying the argument doesn't give you a number not in the list, which means the argument doesn't work.

>>11749752
Sauce? Looks like a VN

>>11749752
>0.999 is equal to one

>>11750177
nvm found it. Sauce is Wonderful Everyday for those interested.

>>11749752
>Why do brainlets refuse to accept that 0.999... = 1?

Because it isn't. I show people the proof in the pic, and they would rather argue that 0=1 than admit that they were wrong. The Real set was INVENTED as a method of ignoring infinitesimals. Therefore any argument using the Real set to claim that 0.999... = 1 is circular logic.

>>11750132
How can an argument that says a string can't be in a list of strings not work if we both agree that the string can't be in the list of strings the argument says it can't be in?

>>11750203
>How can an argument that says a string can't be in a list of strings
Ok but you want this argument to be about real numbers and the strings to stand for the reals. Sure you can get a string that's not in the list, but I'm wondering is there a construction to get a real number that's not among the real numbers represented by the strings in the list?

>>11750216
I didn't want that argument, but sure, the fraction 1/3 can't be indexed by any natural number.

>>11749752
Because that's literally how real numbers work dingus

>>11750239
what

>>11750244
The real number 1/3 is not represented by any string in the list we've been talking about.

>>11750252
I was talking about an arbitrary attempted list of real numbers, not a specific list. There are lists of real numbers such that applying diagonal construction to the list gives you a number in the list and that 1/3 is in the list.

>>11749752
Because they're retarded enough to assume that their feelings about the numbers have anything to do with how they act.
"I like, totally, like think like .9... like is like less than like 1 because like numbers are hard tee hee!"

>>11750276
Can you describe one that doesn't exclude almost all of the real numbers?

>>11750338
No lol, of course not but that's not a proof.

>>11750183
50%, either it is or it isn't

>>11750341
A proof of what? We're talking about a list that includes all real numbers, right?

>>11750351
is 0.999 the schrodinger's 1?

>>11749752
because early math education does not establish the distinction between physical constants and numerators.

so people new to math, have an instinctive understanding of math from a physics interpretation, and that math should represent the reality, and teachers so invested in the subject of "math" don't acknowledge that math has no physical relation, and that new students don't expect that "math" is just an imaginary self-justifying system that doesn't need to represent reality.

i'm sure brainlets would accept it, if they understood that math was just a tool that only has justify itself and forget about reality.
it would make it easier for the brainlets too, not having to try and meld maths and physics to learn basic maths.

Physics is a parasite on math.

>>11750357
A proof that for any countable list of real numbers there is a real number not in the list.

>>11749752
because they don't understand that strings of digits are not literal numbers, just representation of them. they look at the equation and they see "two numbers which are different are the same" which is contradictory.
also because they think 0.999... is not a constant, but a sequence. which wouldn't be *that* bad, but schizos' understading of sequences are shaky at best and they picture it as a literal process in real time, a process which is ""desperately"" trying to reach the end state, but never finishes, no matter how hard he tries. it's poetic.

>>11750369
pretty much this

>>11750382
The list {1,2,3,..} is a countable list of real numbers and misses almost every real number.

>>11750412
>for any

>>11750444
No one disputes the fact that any countable subset of the real numbers is countable.

>>11750471
The question is not whether every countable list of reals is countable. The question is whether every countable list of reals does not contain at least one real.

>>11750209
Wrong

>>11750477
Every list of reals, whether countable or uncountable, certainly contains at least one real. Unless it's the empty set of reals.

>>11749752
Retarded

>>11749752
The fact that the sequence even begins with 0.9 means that it is destined to be less than 1.

>>11750504
no, actually it means that it's destined to be ≤ 1

>>11750504
Fascinating. What about the sequence 0.9+0.9+0.9 which also begins with 0.9? Do they share a common destiny?

>>11750520
0.9+0.9+0.9=0.999
0.999 <1

[eqn]
n = 0.9999...
10n = 9.9999...
9n = 9
n = \frac{9}{9} = 1
[eqn]

What's wrong with this idea? Could you please disprove or invalidate this?

>>11750504
"if a decimal representation of a real number starts with 0.9, then the number is less than 1"
prove this statement

>>11750536
>10n = 9.9999...
this needs elaboration. it's true, but it's not immediate.

>>11749752
I stopped coming here months ago and you people are still talking about the same topic. 4chan truly is worse than Hollywood

>>11750530
>0.9+0.9+0.9=0.999
even the first two plusses = 2.7
way over 1.

>>11750541

Ok so what exactly do I need to prove in this? I'm sorry if this is a brainlet question, I don't exactly see in what direction I'm supposed to elaborate.

>>11750498
You misunderstood what anon said. The question is whether or not for every countable list of reals there is a real number not in the list.

>>11750543
Literally me. I came here to see if there was any neat SpaceX shit up, bam, top of the first page. Fuck you niggers, im going back to /diy/

>>11750545
>even the first two plusses = 2.7 way over 1.
Prove it

>>11750555
That's trivially false. {1,2,3,...} is a countable list of reals and there is a real number not in the list.

>>11750571
0.9+0.9+0.9=2.7

>starts with .9
>is 1

>>11750599
>starts with o
>is 1

>>11750581
Wrong

>>11750575
AAAAAAAAAAAAAAAH YOU ARE FUCKING RETARDED!!!!!!!!!!!!
YOU RUINED MY DAY WITH YOUR RETARDATION!!!!!
ENJOY THE REST OF YOUR DAY WITH YOUR DEMON PEA-BRAIN!

>>11750622
Which part of the text I wrote do you disagree with?

>>11750640
LITERALLY YOUR EVERY POST!!! YOU DON'T EVEN KNOW HOW TO FORM A NEGATIVE OF A STATEMENT! JESUS FUCKING CHRIST ANON!!!!

>>11750640
He can't disagree. He's wrong. He wrote what he wanted to say incorrectly and now he's suffering the consequences.

>>11750652
>>11750653
Quote the text you disagree with. Shouldn't be hard. Cheat code: c

>>11750664
command-c

>>11750653
>>11750664
>The question is whether or not for every countable list of reals there is a real number not in the list
WHAT IS THE NEGATIVE OF THIS STATEMENT ANON!? THE NEGATION OF IT STATES THAT THERE EXISTS A COUNTABLE SET SUCH THAT THERE ***IS NOT*** A REAL NUMBER THAT IS NOT IN THE LIST, AND~~~~~~NOT~~~~~THAT THERE IS A LIST OF REAL NUMBERS SUCH THAT THERE IS A NUMBER NOT IN THE LIST.
>That's trivially false. {1,2,3,...} is a countable list of reals and there is a real number not in the list.
FUCKING HELL. ONE MORE POST FROM YOU AND I SWEAR TO GOD...

>>11749752
>>11749932
1/3 = 0.3333... to infinity, right? The decimals go to infinity because in base 10, you never reach the true value of the limit (get it? Infinite > never ending > can't reach it). Instead it's (not very well) understood that there's a tiny 1/3 of a digit at the end that is rounded off because it can't be expressed in base 10.

So you add 0.333... to 0.333... to 0.333, and 3 tiny rounded off 1/3s make that different between 0.999... and 1

>Inb4 the 1/3s don't count cause muh.. muh.. REEEE
Isn't 2/3 expressed as 0.666...7? Ah, the 2/3 of the last digit are rounded up this time. They're there

>>11750675
>for every countable list of reals there is a real number not in the list
And as I said, this is trivial. Who cares?

>>11750713
>Isn't 2/3 expressed as 0.666...7?
no. and your whole post is wrong.

>>11750726
can you prove it ?

>>11750713
>you have to round up bc its infinite
omfg

1/3 = 0.333...
0.3333 x 3 = 0.999999...
1/3 x 3 = 1
0.99999... = 1

>>11750713
>you never reach the true value of the limit
what does "reaching the true value of the limit" mean ? please explain it in mathematical terms

>>11750734
That ship sailed in the 19th century.

>>11750729
no u

>>11750736
Literally not what I said. Nice reading comprehension, no wonder you think 0.999=1

>>11749752
then is reality would infact be a simulation cause it would run like an old TI82 simulation that saves computing power. no

>>11750746
Nigger are you familiar with asymptotes? Don't be coy. It's not cute.

You can consider 1/3 as the true value, and 0.333... as something that approaches that value as you further extend the infinite chain of digits, but it never reaches that asymptote.
Hence the infinite struggle, cause you're never done, cause you never reach it. If you reached it you wouldn't have to keep going.

>>11750792
>0.333... as something that approaches that value as you further extend the infinite chain of digits, but it never reaches that asymptote.
this is not what 0.333... means though

>>11750653
>>11750675
I think you may be confused.

No one cares if every countable list of reals can be counted, because all those lists are countable by definition. It's a tautology

The thing that people care about is if any list of ALL reals can be countable.

>>11749752
I blame N. Bourbaki.