4
$\begingroup$

I have read that addition, subtraction, multiplication, exponentiation and division are considered the fundamental operations in math.

Has this notion been made precise? Ie. is an operation considered fundamental if it cannot be defined in terms of other fundamental operations?

Can we know these are all the fundamental operations?

Is it possible to define complex conjugation in terms of the other five operations?

  • 8
    These are usually considered the four fundamental operations of *arithmetic*. I don't think I would describe them as the fundamental operations of *mathematics*.2011-06-18
  • 0
    Well, can there be more operations which are not expressible in terms of the others, or are these 4 the only?2011-06-18
  • 2
    There are an enormous number of different operations used in mathematics, acting on many different sets of objects. You mention complex conjugation, but there are also things like square root, logarithms, absolute value, composition of functions, matrix transpose, vector norm, matrix determinant, dot product, cross product, and so forth. Some of these can be described in terms of the four basic arithmetic operations, and some of them can't.2011-06-18
  • 4
    $x - y = x + ((-1)\times y)$ or $x/y = x \times y^{-1}$ show that subtraction and division are not *fundamental* in the sense of not being defined in terms of the others.2011-06-18
  • 1
    and $x+y=x-(0-y)$...2011-06-19
  • 1
    @JimBelk Are there fundamental operations of mathematics?2012-09-13
  • 0
    Not sure the answers given here are correct.2013-12-20

3 Answers 3