Infinitely Many Missing Numbers

The limited precision of fixed point (and floating point) expressions is a problem for programmers. Even with 64-bit double precision floating point (such as Java data type double) precision is limited. Only 264 numbers can be represented. This is a lot, but between any two numbers that are represented there are an infinite number of real numbers that are not represented!

(If your calculus is a little vague, don't worry. Just think about the nearly infinite number of atoms between any two marks on even the most precise ruler.)