# Elementary operations

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?

• Yes, yes! : ) $\,$ Nov 7 '14 at 1:26
• most Definitely! Define as many new operations as you want!
– Joao
Nov 7 '14 at 1:28
• There are many contest problems that start with something like "Let $a\#b=a^2-b$…" or something like that. Nov 7 '14 at 1:36

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