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**SlipEternal** You can define a different addition and multiplication that do not work like regular addition and multiplication. We turn addition and multiplication into abstractions called binary operators. Binary operators are functions on two variables that return one variable. The phrase a set is "closed" under a binary operator means that if we apply the binary operator to any two elements of a set, we get another element of that set. So, we define a binary operator that works like I showed in the post above. That is what $:=$ means. It means it is defined to be equal. So, rather than defining addition as the normal integer addition, we can define a "variant" addition. That turns the element $2(0)+1$ into the "zero" element and $2(1)+1$ into the "unit" of the ring. Notice that I used a different symbol for the addition and multiplication operators. I used $\bigoplus$ and $\bigotimes$ rather than $+$ and $\times$. That was to differentiate between "normal" addition and multiplication from the addition and multiplication that I defined for this problem.

To see how I format math symbols, you can Reply With Quote to one of my replies and it will show you how I formatted it.