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Envy is an emotion which occurs when a person lacks another's quality, skill, achievement, or possession and either desires it or wishes that the other lacked it. [1] Envy can also refer to the wish for another person to lack something one already possesses so as to remove the equality of possession between both parties.
Many dictionary definitions include a reference to envy or envious feelings. In fact, the overlapping use of jealousy and envy has a long history. The terms are used indiscriminately in such popular 'feel-good' books as Nancy Friday's Jealousy , where the expression 'jealousy' applies to a broad range of passions, from envy to lust and greed.
Since taking the square root is the same as raising to the power 1 / 2 , the following is also an algebraic expression: 1 − x 2 1 + x 2 {\displaystyle {\sqrt {\frac {1-x^{2}}{1+x^{2}}}}} An algebraic equation is an equation involving polynomials , for which algebraic expressions may be solutions .
One of the basic principles of algebra is that one can multiply both sides of an equation by the same expression without changing the equation's solutions. However, strictly speaking, this is not true, in that multiplication by certain expressions may introduce new solutions that were not present before. For example, consider the following ...
The word problem for free bounded lattices is the problem of determining which of these elements of W(X) denote the same element in the free bounded lattice FX, and hence in every bounded lattice. The word problem may be resolved as follows. A relation ≤ ~ on W(X) may be defined inductively by setting w ≤ ~ v if and only if one of the ...
An algebraic theory consists of a collection of n-ary functional terms with additional rules (axioms).. For example, the theory of groups is an algebraic theory because it has three functional terms: a binary operation a × b, a nullary operation 1 (neutral element), and a unary operation x ↦ x −1 with the rules of associativity, neutrality and inverses respectively.
Self-envy is produced by 'child part self-objects', self representations from early development that remain split off from the self and harbor destructive and envious feelings toward the creative aspects of the self and results from direct aggressive attacks by these childhood self-objects against the part of the self identified with a ...
By definition, equality is an equivalence relation, meaning it is reflexive (i.e. =), symmetric (i.e. if = then =), and transitive (i.e. if = and = then =). [33] It also satisfies the important property that if two symbols are used for equal things, then one symbol can be substituted for the other in any true statement about the first and the ...
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