Is the “infinity” between numbers actually infinite?

Question

Can numbers get so small (or so large) that there is kind of a “planck length” effect where you just can’t get any smaller? Or is it really possible to have 1.000000…(infinite)1

EDIT: I know planck length is not a mathmatical function, I just used it as an anology for “smallest thing technically mesurable,” hence the quotation marks and “kind of.”

In: 87

Answer 1

There is a 0.99 inbetween 0.9 and 1.

There is a 0.999 inbetween 0.99 and 1.

There is a 0.99999999999999999999 inbetween 0.9999999999999999999 and 1.

You can keep going on as long as you want and adding as many numbers inbetween 0.9 and 1 as you want. There are infinitely many numbers inbetween the two. But! Note that all of those are numbers that end. You can have 0.9 with a billion 9s, and that’s still a specific number that fits somewhere in the middle there.

However, the number 0.9 repeating (or 0.9…) is literally and exactly equal to 1, because if the 9s are infinite then there is nothing inbetween 0.9… and 1, which makes them the same thing.