I am myself, but I am not equal to myself. What am I?
Look at the tags.
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Based on the tags indicating this is a mathematical puzzle, I believe the answer is:
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."