Using only math symbols (no functions like sin, cos, log, etc.) create an expression with only two 2s equal to 5 (no other digits or constants).

"The "+" operation is a function. The word "function" in mathematics is a very general one.  The word "operation" almost always means "a function with exactly two inputs".

The "+" operation is really a function that takes two inputs and returns the sum of those inputs.  In a more formal system, just as we write: f(x), we might have written +(5, 4) = 9.

There are a couple of reasons that the common operations are written with the infix (rather than prefix) operators like "+", "-", "x" and "/".

First off, they were used LONG before anyone had formalized the idea of a function.  Second, by agreeing on some precedence rules you can avoid writing so many parentheses.  So instead of writing: 3+4+5+6

we'd have to write something like +(3, +(4, +(5, 6)))

There is nothing that says that a function has to have a name that's an alphabetic variable, although it is usually done that way.  As your friend points out, square-root is also a function (and again, an ancient and important one) that uses a strange symbol in place of a letter. (My note: the symbol for sqrt evolved from the letter R)

Note that exponentiation is also a function that uses yet another
scheme.  There are other examples of weird symbols used as functions, or as operations, but they are from obscure areas of mathematics.

- Doctor Tom, The Math Forum
  <http://mathforum.org/dr.math/>

Edited on October 15, 2005, 2:56 pm

Posted by pcbouhid on 2005-10-15 14:48:23