# Am but not equal

I am myself, but I am not equal to myself. What am I?

Hint:

Look at the tags.

• Why the downvote? Aug 2 at 8:10

NaN (NaN == Nan -> false, but Double.IsNan(NaN) returns true )

• This is the intended solution, but there are likely others. Jul 31 at 19:07
• By the same token, null works as an answer, since null is null is true but null=null is null — in SQL. What language is your answer in? Jul 31 at 20:04
• I generally work in C#, but use SQL a lot, and Javascript when I have no other choice. Aug 2 at 13:08

Based on the tags indicating this is a mathematical puzzle, I believe the answer is:

A function

In mathematics, a function $$f(x)$$ is not necessarily equal to itself when evaluated at different inputs. For example:
$$f(x) = x^2$$
$$f(2) = 4$$
$$f(3) = 9$$
So the function $$f(x)$$ is itself (it has an identity), but is not equal to itself when computed at different values of $$x$$. For example, $$(f(2) ≠ f(3))$$.

This matches the puzzle statement:

"I am myself, but I am not equal to myself."

• Not a good example, would fail immediatelly with very trivial samples e.g. two identical squares when compare points. But in math there might be some generalization of relations (R), when clasic equivalence aRa does not imply a=a.
– z100
Aug 1 at 0:22
• Don't know about programming syntaxes, but I'm aware that such a case is always because equality is not defined for certain type of elements esp. if elements to compare are identic. Fuzzy logic possibly.
– z100
Aug 1 at 0:32