# If $f$ is bijective but undefined at a point, is it a function?

Consider the set $$A = \{x \in \mathbb{Z{\ge_0}}$$ and $$x \in {-2}\}, B = \{f(x)\}$$.

Is $$f: A \to B$$ still a bijection even though $$f(-2)$$ is undefined?

• Try the command \text{ and } to insert a text "and" in math mode. Or use \land (logical and) in math mode for a $\land$. – Theo Bendit Feb 11 at 15:41
• I'm still confused as to the actual question. Is $A$ a set? A function? If the latter, what is its domain? And what does $x \in -2$ mean exactly? If you're looking for curly braces to help define a set, try \{ and \} in math mode. – Theo Bendit Feb 11 at 15:44
• Your question is not at all clear. What are the two sets that you claim are in bijection? What is the proposed bijection between them? – lulu Feb 11 at 15:46
• @TheoBendit see edit – Jossie Calderon Feb 11 at 15:57
• Voting to close the question as it is not clear what you are asking. If you can, please edit for clarity. – lulu Feb 11 at 16:32

A function $$f: A \rightarrow B$$ is a triple ($$f, A, B$$) where $$f \subseteq A \times B$$ satisfying certain properties. So what you should really be asking is, is $$f$$ a bijection between A and B? If $$f(-2)$$ is not defined, this means that $$-2 \notin A$$, so it doesn't have any consequence on whether your function is a bijection between A and B or not.