If you subtract 0 from any number, that number remains unchanged. Hence, the identity of the number is preserved.
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Additive identity: zero. Multiplicative identity: one.
It is the additive identity property of zero.
Yes: it is 0.
No; here's a counterexample to show that the set of irrational numbers is NOT closed under subtraction: pi - pi = 0. pi is an irrational number. If you subtract it from itself, you get zero, which is a rational number. Closure would require that the difference(answer) be an irrational number as well, which it isn't. Therefore the set of irrational numbers is NOT closed under subtraction.
In subtraction, the minuend minus the subtrahend equals the difference.