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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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0 is the identity

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.

The minus sign.

It is 0.

It is the "additive identity".

No. The identity for addition is zero; the identity for multiplication is one.

Zero.

Zero.

Subtraction is not an identity property but it does have an identity property. The identity is 0 and each number is its own inverse with respect to subtraction. However, this is effectively the same as the inverse property of addition so there is no real need to define it as a separate property.

In mathematics, identity is a transformation that leaves an object unchanged. In addition and subtraction, the identity element is zero. Adding or subtracting zero to or from a number will leave the original number. In multiplication and division, the identity element is one. Multiplying or dividing a number by one will leave the original number.

In mathematics, identity is a transformation that leaves an object unchanged. In addition and subtraction, the identity element is zero. Adding or subtracting zero to or from a number will leave the original number. In multiplication and division, the identity element is one. Multiplying or dividing a number by one will leave the original number.

To start with, the identity element of multiplication is 1, that of addition is 0.

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