In a Feb. 14 letter, "Same old arguments recycled," Jim Moore claims that "we believe in the real number system, although it can't be proven" in an effort to argue that faith-based creationism is as valid as scientific-based evolution.
The real number system came from humanity's need to expand our idea of what we mean by "number" when quantifying and explaining things. Consider the caveman who used 6 pebbles to indicate how many raptors were outside the cave; we only have negative numbers because we need to describe things such as really cold weather.
The real number system consists of all numbers that can be written as whole numbers and fractions (e.g., 5, -3/5, 23/4) as well as those that cannot. Our ability to count and then divide numbers into equal parts is a practical proof of the existence of whole numbers and fractions.
It takes a bit of time to explain, but the existence of non-fractions was proven by the Greeks over 2000 years ago (http://en.wikipedia.org/wiki/Irrational_number). Essentially, they showed that SQRT(2) could not be written as a fraction — expanding our notion of numbers forever.
Other mathematicians, particularly Georg Cantor, added much to what we know about real numbers. But rest-assured, they are proven to exist, not based on faith, and are quite useful in our daily lives.