/sci/ - Science & Math

[Anonymous No.15885471]

>the set of rational numbers is countable because you can assign a natural number to each of them
>no, you CANNOT assign a natural number to each real number, there are simply too many of them!
>yes, for every natural number there are infinite rational numbers, but they are countable because.. uhhh... I don't like where this is going... JUST STOP ASKING QUESTIONS

[Anonymous No.15885477]

[Anonymous No.15885478]

>>15885471
If there was a concrete answer to this would it even change anything in mathematics?

[Anonymous No.15885481]

>>15885471
the key difference is that the rationals are definable and therefore we can enumerate through the rationals by their definition, which is just an integer divided by an integer, so we simply cover every possibility. But with “real” numbers, Cantor implicitly assumes the existence of undefinable real numbers, meaning we have no way to describe them. If you restrict the reals to definable numbers, meaning they can be exactly represented by a finite definition, then they are indeed countable.

All uncountability stems from undefinability, that is, nonsense.

[Anonymous No.15885483]

>>15885471
Watch the chicken YouTube video too
Hundreds of thousands of children are being aborted every single year. Tens of thousands of children are being aborted completely legally in 2023 in deep red USA states.
Abortion is still legal in all 50 states and almost nobody is talking about it. The pro life movement is a controlled opposition and not your fren. Please watch this approximately 15 minute long YouTube video on abortion please whether you be pro choice or already pro life https://youtu.be/XGPv66ZqlEQ?feature=shared [Open] [Open] [Open]

Over 6 billion (yes) Chickens are tortured to death every single year in the United States alone in factory farms. And no your Canada Australia or EU country isn't much better. Billions of animals are being tortured to death in factory farms every single year and it's (partially) your fault! Please watch at least the first five minutes of this YouTube video . In it he explains that people who regularly purchase chicken for years straight will almost certainly cause the torturing and murder of hundreds of extra chickens. That blood is all on your hands and would NOT have been shed had you instead decided to boycott animal products / go vegan ! https://youtu.be/brKhhZlUoOc?feature=shared [Open] [Open] [Open]

What are the conditions like in factory farms where over 96% of all animal products in western nations come from? They are mutilated without anesthetic, crammed in dirty, uncomfortable, and crowded conditions, they are artificially inseminated / raped and jacked off, they are slaughtered. Here is a free approximately 2 hours long documentary about factory farming please watch it thank you https://youtu.be/LQRAfJyEsko?feature=shared htfg

[Anonymous No.15885490]

>yes, for every natural number there are infinite rational numbers

nigguh, for every NATURAL number there are infinite natural numbers.

For every n, assign the set of all naturals divisible by n. Now there's an infinite subset of natural numbers for every natural number. Are the naturals now uncountable?

[Anonymous No.15885493]

>>15885471
>every irrational can be represented with a rational sequence
>irrationals are still uncountable because uhhh reasons
sometimes I fucking hate mathematicians
>>15885478
No, but it might make some trannies (transfinitists) 41% themselves

[Anonymous No.15885494]

>>15885483
>raped and jacked off, they are slaughtered
lucky bastards

[Anonymous No.15885507]

>>15885477
>now listen you chud, this table proves that rational numbers are countable
>as you can see, for every row consisting infinite rationals, I assign one natural numbers
>what do you mean I just contradicted myself?

[Anonymous No.15885510]

This is like the tenth thread this week made by a cognitively inadequate zoomer complaining in an asinine manner about getting filtered by elementary first week contents of his undergrad first year analysis course. I can't stand your tiktok-induced brain rot. Industrial society was truly a mistake. No surprise civilization is going down the shitter.

[Anonymous No.15885511]

>>15885507
look at the pink arrows

[Anonymous No.15885513]

>>15885510
ninth post best post

[Anonymous No.15885516]

>>15885510
almost every analysis course hand waves two major points: the proof of reals and the proof reals are uncountable

[Anonymous No.15885521]

>>15885516
>the proof reals are uncountable

Diagonal argument.

Suppose that every real is assigned a natural. Construct a real number x such that, for the nth real number, the nth decimal place of x is equal to the nth real's nth decimal plus one. This number x is different from every listed real number in at least one decimal place, and therefore it is not counted. By contradiction, there does not exist a counting method.

[Anonymous No.15885526]

>>15885521
bullshit trash doesn't prove shit
cantor is evil and worse than hitler

[Anonymous No.15885527]

>>15885521
n+1 idiot

[Anonymous No.15885532]

>>15885471
It's true. Whereas all rational numbers have a description that is finite in length, I can list them all in an order and not miss any. The real numbers include all the numbers that have an infinite length description with no discernable pattern, so if you give me any list of real numbers, I can construct a new real number by having it differ from each previous infinite length number by one digit. This process can be repeated indefinitely, so all the reals can't be listed.

I get you're a dummy, but maybe go watch some pop-math YouTube and learn how proofs work.

[Anonymous No.15885565]

>>15885471
>stupid sexless virgin freaks trolling other stupid sexless virgin freaks with math
Hahaha have sex you pathetic nerds. Oh wait your ugly and have no rizz. Pic rel you're looks match

[Anonymous No.15885687]

>>15885521
>Construct a real number by changing the nth decimal place of the nth real number
you realize that by doing this you go on forever and you never finish to actually "construct" your precious outlier?

[Anonymous No.15885793]

>>15885490
>are naturals uncountable
Yes

[Anonymous No.15885820]

>>15885687
NOOOOOOO IT'S TOTALLY LE REAL DON'T YOU KNOW REALS ARE LE REAL!!!!
NATURALS ARE TOTALLY BOUNDED ABOVED
ACK MY FAULTY CONTRUCTION OF REAL IS KILL

[Anonymous No.15885833]

>>15885687
This. Even when considering the definable reals (which are countable), then no matter what your diagonal number looks like, we can find infinite numbers in the list that look exactly like that number to a seemingly infinite precision. It wouldn’t make sense for the diagonal number to be completely unique at the 1,000th decimal for example, because there should be infinite other numbers that match the diagonal to any arbitrary precision. So the question is: when does the diagonal number become unique? The answer is never, because it can never be constructed.

[Anonymous No.15885868]

>>15885521
LMAO, only retard morons don't realize the diagonal argument is a meme argument.

00000000...
10000000
01000000
11000000
00100000
10100000
01100000
11100000
...
11111111...

Is beyond obvious the representation below is an infinite sequence of 1, +infinite, and that is not a number.

[Anonymous No.15885919]

>>15885868
The diagonal argument is retarded but what it’s getting at is true.
You can just keep adding numbers to make new numbers. You don’t need some dumbass diagonal strategy, just keep growing the numbers exponentially. For every index you can create two new numbers n^index and index^n. If the number is already in the list, exponent each number by the existing index. Continue this process and you will always end up with a new larger number that you haven’t counted yet.

[Anonymous No.15885921]

>>15885919
that is obviously true in a finite context. But assuming you already have an infinite list in the first place, it makes no sense to add to it. All of this shit could just be ignored if we dismissed actual infinities.

[Anonymous No.15885924]

>>15885921
Sure but I think you’re getting at a nugget of truth. Infinity doesn’t exist *right now* but it is *described* by this continuous process. Infinity can’t exist at any given moment it can only be described across continuous time.

[Anonymous No.15886195]

>>15885477
ok, but where are the negative numbers?