When was the last time you picked a random number from an actual real number line?

Try sampling random floats in your programming language of choice and see how long it takes to get an integer (you will eventually get one).

Then consider that floating point numbers represent only a finite subset of the (countably) infinite rational numbers. And then consider that the set of rational numbers is unimaginably smaller than the set of irrational numbers (which is the other part of the reals).

The fact that integers have measure 0 in the set of real numbers only seems confusing if you're thinking of everyday operations rather than thinking about mathematical abstractions.

floating point IS NOT THE REAL NUMBERS. ok thanks. I was indeed thinking in purely abstract terms. I feel as though you've talked down on me; and what's worse, you did it incorrectly (about the wrong thing). comms have failed.