e

e! or e=2.71828182845904523536028747135266249775724709369995... for the rest of us.

There are a few numbers out there in the universe that keep showing up in place after place, that suggests a greater significance. One of those numbers is e. It isn't like one of those integers we see everyday, that we can write out exactly. That is because e is an irrational number - there is no way we could ever write a decimal or fraction for it, out of integers. It just can't be done. It is like it is forever hiding between the cracks, and like Bigfoot, we can never get a really good look at it. Like pi, any decimal for it, would continue on forever and ever, never being perfectly expressed.

Further, e is a transcendental number. No, that does not mean it likes a lot of Ralph Waldo Emerson, though he is pretty awesome himself. It does mean that this is not a number you can express or solve for with algebra. No matter how many (finite) square roots or cube roots or complicated polynomials you have, you just can't get to it with just algebra. It requires infinity and limits. That makes it part of a class of numbers that is normally invisible and unthought of, even if there are an infinite number just between 0 and 1.

But just what can this number do? It is behind exponential growth, and decay. It is the basis of the natural logarithm. The integral and derivative of an exponential is itself. While the integral of the natural log is often necessary even for basic integrals.

e is what we can use to construct any or all of trigonometric functions, even just simple sine waves. It is necessary to calculate interest for banks or other financial institutions. Yes, true, there are ways around it, but that is just what they are, ugly kludges to get around it.

If we had to rebuild civilization with only 4 numbers, e would have to be one of them. It is that important.... and we can't even write it!