Memes are real

im a quantum brainlet and only watched long enough to see him fumble with infinities

perhaps some physics student can chime in

Seems like there aren't many people on here who know much about quantum mechanics. It seems to downright trigger some anons.

told you why you were wrong but I think I know what you meant.

It is "unknown" whether there is any size of infinity in between the size of the integers and the size of the reals. The continuum hypothesis asserts that no such in between size exists.

By "unknown" I mean that the continuum hypothesis cannot be proved or disproved using the axioms of ZFC.

Yea I realized that after that the CT isn't about whether or not there are ANY other sizes of infinity as I initially thought but rather it's about whether or not there is an infinity SPECIFICALLY in between the integers and the reals.

>It seems to downright trigger some anons.
you're damned right. i guess their belief the universe is fundamentally deterministic helps them cope with their autism. at any moment you can find a thread made by one of these characters ranting and raving about hard determinism.

Yea I used to post on here allot and I remember seeing them. I remember when that experiment was doing pretty much destroying local hidden variable theories related to entanglement and people were all worked up.

To elaborate why there are the same number of transcendental numbers as irrational number, the union of sets of the same cardinality is the same cardinality as the sets.

We know the rational numbers are countably infinite.

Consider the set of finite polynomials where the largest degree is less than or equal to any of the rational coefficients (which may be 0). These sets are clearly countable. The union of these sets is also countable. Each polynomial corresponds to a root which is algebraic number, so the number of algebriac numbers are countable or finite (intuitively not finite, so it's countable).

Since the real numbers are uncountable and composed of algebraic and transcendental numbers, it follows that the set of transcendental numbers are uncountable.

Similarly, the real numbers are composed of the countable rationals, and irrationals. So the set of irrational is uncountable.

So the transcendental numbers and irrational numbers have the same cardinality, so there is the same amount of them.

>the union of sets of the same cardinality is the same cardinality as the sets.
???

no, it's because the transcendental numbers aren't bijective and the irrational numbers are bijective

*for a union of infinite sets

countably infinite at that.

are you retarded, the irrational numbers have cardinality aleph-one. The transcendental numbers are a subset of the real numbers so must have a cardinality of at most aleph-one. It clearly isn't aleph-zero, and it clearly isn't finite. so it's aleph-one.

I think this is what you are trying to say
proofwiki.org/wiki/Countable_Union_of_Countable_Sets_is_Countable

>brainlets arguing about quantitative philosophy

Jealous much? I feel bad for you OP. You have my pity.

>there are infinitely many infinities
How infinite though :^)

>the irrational numbers have cardinality aleph-one
Please think before you make literally unprovable statements.

Real numbers have cardinality aleph-one
Rational numbers have cardinality aleph-zero
Irrational numbers make up the rest of the reals
Therefore, the irrational numbers have cardinality aleph-one, assuming continuum hypothesis.

WE

>assuming continuum hypothesis
Yes, that's the thing that's unprovable, and it's misleading to bring up in this context. The fact that the cardinality of the irrationals equals the cardinality of the transcendental numbers does not rely on CH.

Can someone explain what NDT said or what he meant to say for brainlets like me? Why would there be more transcendental numbers than irrationals?

>Why would there be more transcendental numbers than irrationals?
There aren't. This is easily proven by realizing that the transcendental numbers are a subset of the irrational numbers, so they cannot be a larger set. NDT is just being a brainlet.

OP I hate niggers too but this is pathetic. Just stop.

Transcendental numbers are all irrational numbers. To say there are more transcendentals than irrationals is like saying there's more apples than there are fruit.

NDT probably meant that there are more transcendentals than non-transcendental irrationals

this transcendental/irrational blunder was predicted by pic related, an image that has existed for years

you people aren't properly excited about this meme becoming real