Zeno for the computer age
If you wish to better understand Zeno's worry about the continuum, you could do worse than to consider loops in software. Case 1: You want to loop over 10 records. You write: for i from 1 to 10 process_record() What could be simpler? OK, let's loop over the positive integers, finding the prime numbers: for i from 1 to ∞ check_for_primality() This loop will run forever, but it is a perfectly valid loop. We can even set it up to loop over all integers: j = 0 for i from 0 to ∞ j = j - 1 print i print j And with only a little more trouble, we could loop over the rational numbers as well. But what if I ask you to loop over the real numbers between, say, 0 and 1? The problem here is much worse than the loop running forever: the loop can't even get started. We could print out "0"... and then what? There is no "next" real number to which we can proceed. And note: the concept of a lim...