> zero has many properties that other numbers do not
In particular, zero is the additive identity [0] in almost all the "usual" number systems in which it appears. That is roughly speaking, it is the only A such that X + A = X, for all X, where X and A are elements of the number system (e.g. field of real/complex numbers).
The integers form a group under multiplication though and a key property of a group is that every element has an inverse. So how does the definition hold if there is nothing that could be considered an inverse for the number 0? Curious about this... I never thought about it before.
In particular, zero is the additive identity [0] in almost all the "usual" number systems in which it appears. That is roughly speaking, it is the only A such that X + A = X, for all X, where X and A are elements of the number system (e.g. field of real/complex numbers).
[0] https://en.wikipedia.org/wiki/Additive_identity