Definition of Inverses. Meaning of Inverses. Synonyms of Inverses

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Definition of Inverses

Inverse
Inverse In*verse", a. [L. inversus, p. p. of invertere: cf. F. inverse. See Invert.] 1. Opposite in order, relation, or effect; reversed; inverted; reciprocal; -- opposed to direct. 2. (Bot.) Inverted; having a position or mode of attachment the reverse of that which is usual. 3. (Math.) Opposite in nature and effect; -- said with reference to any two operations, which, when both are performed in succession upon any quantity, reproduce that quantity; as, multiplication is the inverse operation to division. The symbol of an inverse operation is the symbol of the direct operation with -1 as an index. Thus sin-1 x means the arc whose sine is x. Inverse figures (Geom.), two figures, such that each point of either figure is inverse to a corresponding point in the order figure. Inverse points (Geom.), two points lying on a line drawn from the center of a fixed circle or sphere, and so related that the product of their distances from the center of the circle or sphere is equal to the square of the radius. Inverse, or Reciprocal, ratio (Math.), the ratio of the reciprocals of two quantities. Inverse, or Reciprocal, proportion, an equality between a direct ratio and a reciprocal ratio; thus, 4 : 2 : : 1/3 : 1/6, or 4 : 2 : : 3 : 6, inversely.
Inverse
Inverse In*verse", a. [L. inversus, p. p. of invertere: cf. F. inverse. See Invert.] 1. Opposite in order, relation, or effect; reversed; inverted; reciprocal; -- opposed to direct. 2. (Bot.) Inverted; having a position or mode of attachment the reverse of that which is usual. 3. (Math.) Opposite in nature and effect; -- said with reference to any two operations, which, when both are performed in succession upon any quantity, reproduce that quantity; as, multiplication is the inverse operation to division. The symbol of an inverse operation is the symbol of the direct operation with -1 as an index. Thus sin-1 x means the arc whose sine is x. Inverse figures (Geom.), two figures, such that each point of either figure is inverse to a corresponding point in the order figure. Inverse points (Geom.), two points lying on a line drawn from the center of a fixed circle or sphere, and so related that the product of their distances from the center of the circle or sphere is equal to the square of the radius. Inverse, or Reciprocal, ratio (Math.), the ratio of the reciprocals of two quantities. Inverse, or Reciprocal, proportion, an equality between a direct ratio and a reciprocal ratio; thus, 4 : 2 : : 1/3 : 1/6, or 4 : 2 : : 3 : 6, inversely.
Inverse
Inverse In*verse", a. [L. inversus, p. p. of invertere: cf. F. inverse. See Invert.] 1. Opposite in order, relation, or effect; reversed; inverted; reciprocal; -- opposed to direct. 2. (Bot.) Inverted; having a position or mode of attachment the reverse of that which is usual. 3. (Math.) Opposite in nature and effect; -- said with reference to any two operations, which, when both are performed in succession upon any quantity, reproduce that quantity; as, multiplication is the inverse operation to division. The symbol of an inverse operation is the symbol of the direct operation with -1 as an index. Thus sin-1 x means the arc whose sine is x. Inverse figures (Geom.), two figures, such that each point of either figure is inverse to a corresponding point in the order figure. Inverse points (Geom.), two points lying on a line drawn from the center of a fixed circle or sphere, and so related that the product of their distances from the center of the circle or sphere is equal to the square of the radius. Inverse, or Reciprocal, ratio (Math.), the ratio of the reciprocals of two quantities. Inverse, or Reciprocal, proportion, an equality between a direct ratio and a reciprocal ratio; thus, 4 : 2 : : 1/3 : 1/6, or 4 : 2 : : 3 : 6, inversely.
Inverse
Inverse In"verse, n. That which is inverse. Thus the course of human study is the inverse of the course of things in nature. --Tatham.

Meaning of Inverses from wikipedia

- Look up inverse in Wiktionary, the free dictionary. Inverse or invert may refer to: Inverse (logic), a type of conditional sentence which is an immediate...
- inverse. This lack of inverses is the main motivation for extending the natural numbers into the integers. An element can have several left inverses and...
- "right-invertible" in which one-sided inverses are considered.) The linear transformation mapping x to Ax is invertible, i.e., it has an inverse under function composition...
- and right inverses, if they exist, will agree, and the additive inverse will be unique. In non-****ociative cases, the left and right inverses may disagree...
- and Drazin inverses" (PDF). Matematički Vesnik. 49: 163–72. Golub, G. H.; Pereyra, V. (April 1973). "The Differentiation of Pseudo-Inverses and Nonlinear...
- when it exists, a modular multiplicative inverse is unique: If b and b' are both modular multiplicative inverses of a respect to the modulus m, then a b...
- This iteration can also be generalized to a wider sort of inverses; for example, matrix inverses. Every real or complex number excluding zero has a reciprocal...
- {\displaystyle \{1,3\}} -inverses are exactly those for which X = 0 {\displaystyle X=0} , and the { 1 , 4 } {\displaystyle \{1,4\}} -inverses are exactly those...
- functions, under suitably restricted domains. Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions...
- A left inverse in mathematics may refer to: A left inverse element with respect to a binary operation on a set A left inverse function for a mapping between...