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0, zero, is defined as the identity element for addition and subtraction.

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While 0 is certainly the identity element with respect to addition, there is no identity element for subtraction. The identity element of a set, for a given operation, must commute with every element of the set.

Since a - 0 ≠ 0 - a, according to group theory, 0 is not an identity with respect to subtraction.

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Q: What is the identity element for addition and subtraction?
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