math

[Alan]

I was thinking lately about math related programming. The I had an interesting thought. (I don't really know the answer). What if multiplication, division and order of operands did not exist? Would we know it? My question is: "Does every formula have a equivalent counterpart that uses 1.) no multiplication 2.) no division and 3.) implies no order of operands. I have not been able to find any yet for even rudimentary formula.

But Obviously... Multiplication can easily be replaced with addition:
4*5 = 4+4+4+4+4 = 5+5+5+5 ... a * b = (i=1,i≤a)Σ(b)

etc... What are your thoughts?

[helios]

What if multiplication, division and order of operands did not exist? Would we know it?

I'm not sure what you mean.

Precedence rules are artificial and arbitrarily defined, not intrinsic to mathematics. They're a feature of mathematical notation, just like the plus sign, and Arabic numerals. For example, reverse polish notation doesn't need precedence, just operators with fixed and known arity (http://en.wikipedia.org/wiki/Arity ).

Addition and multiplication are special cases of hyperoperation (http://en.wikipedia.org/wiki/Hyperoperation ).
Integral division can be performed as repeated subtraction and counting. Arbitrarily precise rational division is slightly more complicated.

Really, this belongs in the lounge.