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

They really are infinite because you can always add another decimal place. Take the gap between 1 and 2.

Halfway is 1.5.
Another fractional step towards 2 would be 1.51.
Another would be 1.511.
Another would be 1.5111.
Another would be 1.51111.

There’s nothing stopping you from adding yet another “1” to the end of the number. Sure, it’s such a small piece of a number that most people would ignore it and round, but that doesn’t mean it doesn’t exist.

So yes, it’s infinite.