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Visual proof of the Pythagorean identity: for any angle , the point (,) = (, ) lies on the unit circle, which satisfies the equation + =.Thus, + =. In mathematics, 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 ...
In psychology, introjection (also known as identification or internalization) [1] is the unconscious adoption of the thoughts or personality traits of others. [2] It occurs as a normal part of development, such as a child taking on parental values and attitudes. It can also be a defense mechanism in situations that arouse anxiety. [2]
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In constructive mathematics, "not empty" and "inhabited" are not equivalent: every inhabited set is not empty but the converse is not always guaranteed; that is, in constructive mathematics, a set that is not empty (where by definition, "is empty" means that the statement () is true) might not have an inhabitant (which is an such that ).
In sociology and other social sciences, internalization (or internalisation) means an individual's acceptance of a set of norms and values (established by others) through socialisation. Discussion [ edit ]
In mathematics, an identity element or neutral element of a binary operation is an element that leaves unchanged every element when the operation is applied. [1] [2] For example, 0 is an identity element of the addition of real numbers. This concept is used in algebraic structures such as groups and rings.
It is not a relation between propositions, and is not concerned with the meaning of propositions, nor with equivocation. The law of identity can be expressed as (=), where x is a variable ranging over the domain of all individuals. In logic, there are various different ways identity can be handled.
In the philosophy of mathematics, Benacerraf's identification problem is a philosophical argument developed by Paul Benacerraf against set-theoretic Platonism and published in 1965 in an article entitled "What Numbers Could Not Be". [1] [2] Historically, the work became a significant catalyst in motivating the development of mathematical ...