Elementary operations

Question

There are four elementary arithmetic operators. Are all operations in mathematics derived from the four elementary arithmetic operators?

I'm studying linear algebra and noticed that some exercises define a new operation such as "adition between (a,b) and (c,d) is (a+d, c+b)". Is there a freedom in mathematics to define new operations at wild?

There are many contest problems that start with something like "Let $a#b=a^2-b$…" or something like that. — Akiva Weinberger, Nov 07 '14 at 01:36

score 1 · Answer 1 · answered Nov 07 '14 at 01:38

1

I'm not an expert in this field, although I don't think all of the operations in the integers can be expressed in terms of those.

For example consider the operation $a\star b$ which is defined to be the $a$'th prime larger than $b$.

answered Nov 07 '14 at 01:38

Asinomás

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Elementary operations

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