Motivation: Motivation for the Proof of Uniqueness of Zero

(related to Proposition: Uniqueness of Negative Numbers)

It might seem strange that one has to prove the uniqueness of negative numbers. It would be very surprising if they were not unique. However, this is something we probably only take for granted, because we have been taught in the school not to ask such "silly" questions or just because we never experience that after spending 10€ out of 100€ we never find another amount of money left in our purse than 90€.

But our daily experience might be wrong! How can we +be sure+ that this disaster will never happen? Could it be that, one day, we will find something else than 90€ in our purse, just because we spent "another" or the "wrong" 10€? Well, unfortunately, the uniqueness of negative numbers, can be proven, +assuring us+ that the result is always the same and correct, whenever we calculate with negative numbers. The uniqueness of negative numbers follows in a simple way from the axioms of addition.

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