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Please excuse my shameful ignorance, but this is something I've always wondered:
The set of all real numbers is infinite.
The set of all prime numbers is also infinite.
Yet the set of all prime numbers is a subset of the set of all real numbers.
But how can there be more real numbers than prime numbers if there are an infinite number of both of them?
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doesn't know the difference between countable and uncountable infinity
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>>8048942
>more
There aren't more. More implies a quantity. We're not dealing with quantities, we're dealing with set cardinality. The basic premise is the one grows an infinite ratio faster than the other.
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Prepare your anus
https://www.youtube.com/watch?v=BBp0bEczCNg
https://www.youtube.com/watch?v=FVZqPaH94qU
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>>8048942
The set of prime numbers can be mapped, 1-to-1, to the set of positive integers. The set of prime numbers is thus countable.
The set of real numbers is not countable. See Cantor's diagonal argument (https://en.wikipedia.org/wiki/Cantor's_diagonal_argument). Because the primes are countable but the reals are not, there are more reals than primes (the reals are a higher-order infinity).
Thus, the size of the infinite set of primes is the same as the size of the infinite set of integers, but both are smaller than the infinite set of reals.
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>>8048952
>grows
they don't grow. they ARE more.
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>>8048958
>mfw
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>>8048967
what are you talking about? your post is disconnected nonsense
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>>8048967
Not the guy you responded to. You state that there is a bijective mapping between N and R. You're saying that R is countable?
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>>8048977
I'm saying "just is" logic is completely unhelpful for explaining why cardinality is a thing. You don't say the mapping "just is" and be done with it, you have to discuss why one mapping is exhausted per the other. "Oh well they ARE more" does nothing but restate the premise OP is having trouble with.
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>>8048997
the whole sentence was
>they don't grow. they ARE more.
because they don't fucking "grow"
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>>8049010
Then the mapping grows. I understand why it's an issue for you, there's just no simpler way to say it.
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>>8049018
nothing grows
the set is just bigger
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>>8049026
No it isn't. There are not "just is"'s in mathematics.
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>>8049079
What are you on about?
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