Negation of there exists quantifier? The problem states to find the negation of the following statement:

There exists a number which is equal to its square.

Original Answer: There does not exist a number which is equal to its square.
My answer: There exists a number which is not equal to its square
Are both the answers above equal? if not then what am I missing? To me both the answers are not equal from a mathematical point of view.

This will be helpful to understand negation:
Statement with universal quantifier: $\forall x, p(x)\implies q(x)$.
It's negation is $\exists x, p(x)\land \lnot q(x)$
Statement with existential quantifier: for some $x, p(x)\land q(x)$.
It's negation is $\forall x, \lnot p(x)\lor \lnot q(x)$ which is further equivalent to
$\forall x, p(x)\implies \lnot q(x)$.

Your statement is "for some $x$, $ x$ is a number and $x^2=x$."

It's negation will be "$\forall x$, if $x$ is a number then $x^2\ne x$" which when formulated in language gives "Every number is not the square of itself."
