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What is the identity property in math?

Updated: 4/28/2022
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The identity property exists only in the context of a set (such as integers or rationals or reals) AND a binary operator (such as multiplication or addition).

The identity property of a set with the binary operation # states that there is a unique element in the set, called the identity which is denoted by i, such that

x # i = i # x = x for all elements x is the set.

In the sets mentioned above,

the additive identity is 0;

the multiplicative identity is 1.

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Q: What is the identity property in math?
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