Question

I will award medal for the best answer!
Why are there certain conventions in mathematics?
For example, why do we use epsilon in calculus for the small quantity? Why do we use a, b, and c, generally, for constants? And how do such things come about?

Answer 1

People started using it that way, and once they start, they never change. Using conventions make things easier to understand. (Hence why it's hard for some math/physics majors where they seem to screw everything up)

Answer 2

Thanks.

Answer 3

From Wikipedia:

Variables are used in open sentences. For instance, in the formula x + 1 = 5, x is a variable which represents an "unknown" number. Variables are often represented by Greek or Roman letters and may be used with other special symbols.

In mathematics, variables are essential because they allow quantitative relationships to be stated in a general way. If we were forced to use actual values, then the relationships would only apply in a more narrow set of situations. For example:

State a mathematical definition for finding the number twice that of ANY other finite number:
2(x) = x + x or x * 2
Now, all we need to do to find the double of a number is replace x with any number we want.
2(1) = 1 + 1 = 2 or 1 * 2
2(3) = 3 + 3 = 6 or 3 * 2
2(55) = 55 + 55 = 110 or 55 * 2
etc.
So in this example, the variable x is a "placeholder" for any number—that is to say, a variable. One important thing we assume is that the value of x does not change, even though we do not know what x is. But in some algorithms, obviously, will change x, and there are various ways to then denote if we mean its old or new value—again, generally not knowing either, but perhaps (for example) that one is less than the other.

a, b, c, and d (sometimes extended to e and f) usually play similar roles or are made to represent parallel notions in a mathematical context. They often represent constants or coefficients, for example in a polynomial or an equation, which are not completely specified.

\epsilon usually represents an arbitrarily small positive number.
\epsilon and \delta commonly denote two small positives.

http://en.wikipedia.org/wiki/Variable_(mathematics)