Define Identities.
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Identity is the qualities, beliefs, personality, looks and/or expressions that make a person or group. One can regard the awareness and the categorizing of identity as positive or as destructive. A psychological identity relates to self-image, self-esteem, and individuality.
An Identity is an equality relating one mathematical expression A to another mathematical expression B, such that A and B (which might contain some variables) produce the same value for all values of the variables within a certain range of validity. In other words, A = B is an identity if A and B define the same functions, and an identity is an equality between functions that are differently defined.
For example,
and are identities. Identities are sometimes indicated by the triple bar symbol ≡ instead of =, the equals sign.
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