- #1

"Don't panic!"

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Now, for example, if we have ##a## such that ##ax=b## and we want to prove this is unique, we start by assuming the contrary, i.e. that it isn't unique. The general approach to this is to assume that there exists another element ##c## such that ##cx=b## and then show that ##a=c##. Is the reason why we only need to consider the case where one other element satisfies this property (as opposed to several other elements satisfying this same property) because if we assume that just one other element ##b## satisfies the same property as ##a##, but turns out to be equal to ##a## then we have contradicted our assumption that ##a## is not unique, in other words our assumption is false (and since this is binary logic) the contrary must be true, i.e. ##a## is unique.

Is this all there is to it? (Apologies if this is a bit convoluted)