Well, then sin(x) = x if x is infinitely small

> Assuming[x == 0, Simplify[Sin[x] == x]]

Mathematica returns True. And any middle schooler will also tell you it's true.

The only reasonable interpretation of "infinitely small" is that it's zero.

so there's an unconditionally correct answer (it's also equal to abs(x) for x>0), and then there is an answer that is only correct for half the domain, which requires an additional assumption.

sqrt(square(i)) != abs(i)

So no, it’s not unconditionally correct either.