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[Putnam]

There's also infinite irrational numbers.

There's pretty much infinite real numbers in said range.

If given any two non-equal real numbers, there is an infinite number of real, irrational and rational numbers between them.

[Arcvasti]

Its numbers all the way down.

[hops]

But is a number between its-

* Objective explodes

[Helgoland]

There's also infinite irrational numbers.

There's pretty much infinite real numbers in said range.

If given any two non-equal real numbers, there is an infinite number of real, irrational and rational numbers between them.

Even worse, there are exactly as many real numbers between any two numbers as there are in total.

[hops]

So a set of all sets does contain itself?

[Graknorke]

There's also infinite irrational numbers.

There's pretty much infinite real numbers in said range.

If given any two non-equal real numbers, there is an infinite number of real, irrational and rational numbers between them.

Even worse, there are exactly as many real numbers between any two numbers as there are in total.

I thought there were twice as many real numbers between 0 and 1 and 0 and 2.

[Tawa]

There's also infinite irrational numbers.

There's pretty much infinite real numbers in said range.

If given any two non-equal real numbers, there is an infinite number of real, irrational and rational numbers between them.

Even worse, there are exactly as many real numbers between any two numbers as there are in total.

I thought there were twice as many real numbers between 0 and 1 and 0 and 2.

INFINITY KNOWS NO BOUNDS.

[Orange Wizard]

Infinity times two is still infinity. I think.

Numbers are weird.

[Xantalos]

Infinity times two is still infinity. I think.

Numbers are weird.

Yeah, at that point it's basically the opposite of zero.

[Graknorke]

Infinity times two is still infinity. I think.

Numbers are weird.

But it's twice as big of an infinity! That's an important distinction. Or should be, as I see it,

[Tawa]

Infinity times two is still infinity. I think.

Numbers are weird.

But it's twice as big of an infinity! That's an important distinction. Or should be, as I see it,

But infinity is everything! You can't have twice as big an everything because there are no things left.

Kind of like how the "infinity + 1" thing is deeply flawed.

[Graknorke]

You can have an infinite set that isn't everything. I literally gave 2 examples in a post you replied to.

[Tawa]

But it isn't finite! That encompasses everything due to a lack of a boundary.

[penguinofhonor]

.

[Graknorke]

But it isn't finite! That encompasses everything due to a lack of a boundary.

0 to 1 does not encompass everything. Really.