[Alas Babylon!]

OK, so let me get a question/comment in.

Infinite means — never-ending. Goes on forever. Never stops.

So, there are infinite integers and infinite real numbers, correct?

Then, since they never stop, the point is moot. There aren’t more real numbers, because of the state of infiniteness, that never ends.

I don’t see an issue. I simply accept infinite means what it means. You can’t count to infinite, either in integers or real numbers.

[LukeL]

Think of it this way. Between 1 and 1.1 there are an infinite set of numbers, while at the same time there are an infinite set of numbers between 1 and 1.01. Logic tells us there should be ten times as many numbers between the latter but that would mean one set of infinity is larger than another set of infinity.

[Moonman62]

Read this:

https://en.wikipedia.org/wiki/Cantor%27s_diagonal_argument

[unread]

"I simply accept infinite means what it means."

Yeah but, maybe infinite doesn't mean what it means... Like, maybe this isn't Saturday... Maybe it's really Tuesday... Maybe up isn't really that, but in fact, it's down...hmmmm

[IronJack]

Exactly. "Infinity" isn't a number. It's not like you can add infinity plus one. Mathematically, it just means "unbounded."

So the idea of comparing "infinities" is in itself absurd. How can one "forever" be longer than another?

It is correct to say the real numbers is an unbounded (infinite) set. It is also correct to say that the integers are an unbounded set. It is not correct to say that the set of real numbers is greater than the set of integers.

[BlackbirdSST]

You can’t count to infinite, either in integers or real numbers.

Maybe not. If one can get enough taxpayer $$$'s then one can spend a lifetime trying! It beats watching the sex life of some toad.

[CharlesWayneCT]

THere’s this really interesting take on infinity, using an analogy of a hotel and buses, called Hilbert’s Infinite Hotel paradox.