- #1

Logical Dog

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**{a,-a,0} ∈ Z**

*For a set to have inverse under an operation, all elements must be able to be combined with another element of the set under that operation, after which the product of combination under said operation yields the*

**identity element**of that operation.My question is, this is a strict definition, but the set of integers under

**division, does it have an inverse or not?**

0/0=undefined. So, Zero is the element which does not fall under this defnition, indeed, 0/0 is undefined. But the definition must be strictly followed? there is also no element which 0 can be divided by to

**give one...**

Second question about notation, { } are used to denote sets. But if we want to denote generalised elements like a, -a, and 0 and say they are elements of the set of integers, do we use brackets or exclude them?

a,-a,0 ∈ Z

**OR {a,-a,0} ∈ Z**