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

Here’s a counterexample of why the planck length is huge compared to infinitely small numbers: probability will always demand smaller numbers.

For example one roll of the dice has a 1/6 probably of rolling a 4. Two rolls have a 1/36 probability of rolling two 4s. The probability of rolling six trillion 4s in a row is an extremely small number, and it is massive compared to twenty trillion 4s.