Did you know that there are more irrational numbers than there

I did not know that.

And there are the same number of rational numbers as there are positive integers!

Did you know that there is more than one infinity?

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Imagine a square. 2D. Finite. Did you know there's a secret cheat code to the Universe that makes it so, on that square, you can walk in whatever direction and you'll eventually reach the place where you started?

>>1468687
mind = blown

>>1468687
>square
*Sphere FTFY

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Did you know summing together all the natural numbers produces the quantity of -1/12?

did you know that 0.9 (repeating to infinity) is the same number as 1

Is any of this relevant in reality

>>1468639
same

>>1469417
It is, IIRC >>1469257 result is used in quantum mechanics or some other high level physics

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>>1468615
>>1468661
>>1468665
>>1469257
>>1469261
True.

>>1468615
How do you proofs this?
Induction?

>>1470664
Like this:
https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument

>>1469261
No, it will always be almost 1.

>>1471599
Is there a number between .9 repeating and 1?

>>1471599
0.999... is defined to mean the limit of the sequence 0.9, 0.99, 0.999, and so on. All the terms in the sequence are less than 1 but the limit is 1.

>>1471615
>>1471624
.9 repeating is not a single number but in fact an infinite set of all numbers that are greater than .9 but less than 1.

>>1471632
the original post was not discussing a set but rather a number >>1469261

>>1471632
no physicalism b/c of qualia

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Pascal invented a really cool triangle. What a boss...

math sucks

>>1468615
>there's an infinite number of rational numbers
>there's an infinite number of irrational numbers

How can one infinity be larger than the other? That sounds like jewish lies to me.

>>1473620
>That sounds like jewish lies to me
That's funny, because infinities are often represented by the Hebrew letter Aleph.

https://en.wikipedia.org/wiki/Aleph_number
https://youtu.be/elvOZm0d4H0

>>1473620

Wouldn't all infinity be equally infinite?

numbers aren't even truly -real- who cares you NURDS

>>1473683
No, watch the video in >>1473681 or this if you have time https://youtu.be/SrU9YDoXE88

tl;dw there are different kinds of infinity, the simplest difference is between infinities that you could list *in theory*, like natural numbers (1, 2, 3, ...) you can list them without "skipping" any. But with real numbers (which includes pi and other decimals that never end) you can never write a list without skipping an infinite amount.

>>1473707
I fucked up the grammar in this post but I think it's still readable. But here's a corrected version:

There are different kinds of infinity. The simplest difference is between infinities that you could list *in theory*, like natural numbers, (1, 2, 3, ...) which you can list them without "skipping" any, and infinities that you can't list even in theory, like real numbers, (like pi and other decimals that never end) which you can never write a list without skipping an infinite amount.

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>>1473718

I'm probably missing a huge point here by not being a math pro, but defining and comparing infinities by whether or not their parts could theoretically be listed without getting stuck in a pocket infinity like pi seems folly somehow; like trying to put an unreasonable limit on it all to meet human limits. There's gotta be something better than that...

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I look around and all I see is a bunch of NERDS

>>1474109
It's actually not quite "different infinities". Infinity really is just a concept and these "different infinities" aren't actually more or less "infinite" than each other. It's that you can have infinite sets with different cardinalities. What differs is not the infinite-ness, but cardinality.

>>1469257
This is false. Don't believe everything you see on youtube.

>>1475051
It's not false and while you and I both know what video we are talking about, I also believe you and I both know that what is wrong is the video's explanation. The video obviously didn't bother extending functions or go through other assumptions they made due to the nature of its audience but this does not make the result wrong. Here is an article that seems to explain away some of the assumptions, but I admittedly only skimmed through it. https://plus.maths.org/content/infinity-or-just-112

I took calc 2 a month ago it was cool we did stuff with infinity but the class was only a month long and I didn't review it since then and I'm probably going to forget it all

>>1468615
https://youtu.be/3bacYDSy19Q?t=324
>a real number is uncomputable with probability 1 and a real number is computable with probability 0
>in other words if you pick a real number between 0 and 1 at random it is possible that you will get a computable real but it is infinitely unlikely.
>this unit interval, the commutable reals are an infinitesimally small part of this.
>this shows you how insignificant the computable reals are. the only problem is that every real number that we've ever seen or used is a computable real. the uncomputable reals are in a way a mathematical fantasy.
>and to make it worse, because most real numbers we cannot really refer to so they exists only a sense of a fantasy.

https://youtu.be/xaAhPo5KKUI?t=303
>how many possible names or ways are there are to refer to real numbers? its only a countable infinity of possibilities so not just the computable reals have probability 0 but all the nameable real numbers have probability 0 most real numbers will never be nameable in any way at all so they are completely inaccessible.
>Chaitin is trying to argue that real numbers don't exist.

>>1471615
It's
0. ... 1
where
... is an infinite amounts of zeros.

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>>1474657

Ok, that sounds reasonable.

>>1468615
>>1470664


Here is a nice proof :

Assume that f is a bijection between IN and [0;1], then the union of the open intervals of length 1/2^(n+2) and centered arroud f(n) is a covering of [0;1]. However, the total length of this intervals smaller than 1/2. Contradiction.
To be truly honnest you need something more to show the contradiction. You can either use measure theory (which gives a mathematical frame for what length means for complicated subsets of IR) or using the fact that [0;1] is compact and that you can extract a finite covering.

>>1468615
Yes. Did you know that the rational numbers have Lebesgue measure 0 in R?

>>1476647
I didn't even know what a Lebesgue measure was, though after reading it I really should have at least known it existed.

Antispambampo

Did you know you can abuse mathematical terminology to provide dumb bitesize pieces of math to feed to equally dumb people.
The notion of 'cardinality' was developed because it makes no sense to say that one infinite set has more elements than another infinite set.
>inb4 some dumb weeb who used a fraction of his neet time to read a pop-sci book tries to argue with me
Stop, i'm right, you're wrong.

>>1478032
It sounds like you are trying to initiate an argument but maybe I just don't understand what you are trying to say. Sure it makes no sense to say that one infinite set has more elements than another infinite set, but when you know about cardinality you can then say that an infinite does indeed have more elements than another infinite set. Do you have a problem with how the OP is worded or with the phrase "some infinities are larger than other infinities"?

>>1479451
Cardinalities aren't a method by which to say "there is more stuff in this infinite set than that infinite set", thats just how its explained to undergrads. Cardinalities are a solution to the problem of how to classify different bijection groups.
But thats beside the point, OPs claim makes literally no mathematical sense.

are irrational numbers female? (not boys)

>>1479650
I always thought of odd numbers as male and even numbers as female.
Not being a gurl doesn't make you rational.

>>1479645
Would OP's claim be better expressed as the set of all rational numbers is strictly greater than the set of all irrational numbers? Or does it need to be the cardinality of the set of all rational numbers is strictly greater than the cardinality of the set of all irrational numbers?
Just reading through stack exchange posts and the Wikipedia articles it doesn't seem that equating cardinality to size of a set is a bad way to think about it. Considering the informal setting of this site wouldn't equating cardinality to size be appropriate?

>>1479674
1 is an odd number and 0 is an even number so it makes sense.

>>1479835
Dick and pussy.

>>1476636
It can't be a bijection because [0,1] has a different cardinality. Regardless, I like the reasoning behind the proof.

>>1468615

>>1481302
you're such a faggot

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>>1481303
Do you not find it strange that you spend many hours every day trying to make /qa/ angry and yet the only result is you yourself getting angrier and angrier?
Take it easy and try to enjoy things for once in your life.

It's been a while since I've had the course but did you know that a first-order logic system is complete or consistent not both?

>>1468615
Did you know there are more testicles on the planet Earth than there are penises?