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If you subtract zero, you get the original number back.The reason it is not usually considered the "identity element of subtraction" is that the base operations are addition and multiplication - subtraction and division are simply the inverse operations to addition, and multiplication, respectively. When defining numbers in an axiomatic system, the emphasis is on those base operations.

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The identity element must commute with every element in the set under the relevant operation. However, x - 0 = x while 0 - x = -x for any element in the set.

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Q: Why is zero not an identity element in subtraction?
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