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

Yes, the infinity between real numbers is infinite. It’s “more infinite” even than the number of integers for example. The real numbers are said to be “dense” which basically means the same thing—there cannot be two real numbers where there aren’t also numbers in between.