I had to chuckle when I read "as simple as a real number". If we are being strict, anything beyond the natural numbers really introduces quite a puzzle over what on earth is going on.

For example, we cannot represent the value of Pi in Hindu-Arabic notation; it stretches to some 'infinity' which is just bizarre and which we can't capture on paper. Saying it has a value opens up some interesting questions about what a number or a value actually is. I suspect people have very clear opinions which are all different from each other.