# The domain of every function is a subset of R.

just wondering if this statement is true or false? And can anyone give an example // Counter Example if the statement is true or false respectively

• What kind of the function did you mean? – Mikasa Sep 24 '17 at 13:29
• If $A$ and $B$ are sets, then there is a function $f$ with domain $A$ and codomain $B$. – user296602 Sep 24 '17 at 13:29
• x^2; 3x+2; |y|=x – user451844 Sep 24 '17 at 13:36
• @user296602 Unless $B$ is empty and $A$ is not. – Theo Bendit Sep 24 '17 at 13:37
• I expect that $R$ stands for the set of real numbers. The answer to your question is "no". Functions do not have necessarily real numbers as input. – drhab Sep 24 '17 at 13:37

I can just define a function that takes ordered pairs as input by $f((1,2))=3$. Its domain is $\{(1,2)\}$, which is not a subset of $\Bbb R$