reversed in position, order, direction, or tendency.
2.
Mathematics.
a.
(of a proportion) containing terms of which an increase in one results in a decrease in another. A term is said to be in inverse proportion to another term if it increases (or decreases) as the other decreases (or increases).
b.
of or pertaining to an inverse function. Compare direct(def. 16).
3.
inverted; turned upside down.
–noun
4.
an inverted state or condition.
5.
something that is inverse; the direct opposite.
6.
Mathematics.
a.
an element of an algebraic system, as a group, corresponding to a given element such that its product or sum with the given element is the identity element.
a point related to a given point so that it is situated on the same radius, extended if necessary, of a given circle or sphere and so that the product of the distances of the two points from the center equals the square of the radius of the circle or sphere.
d.
the set of such inverses of the points of a given set, as the points on a curve.
–verb (used with object)
7.
to invert.
[Origin: 1605–15; < L inversus, ptp. of invertere to turn upside down or inside out, reverse.See in-2, verse]
reversed (turned backward) in order or nature or effect
2.
opposite in nature or effect or relation to another quantity ; "a term is in inverse proportion to another term if it increases (or decreases) as the other decreases (or increases)" [ant: direct]
noun
1.
something inverted in sequence or character or effect; "when the direct approach failed he tried the inverse"
inverse
Adjective
(ĭn-vûrs')
Relating to a mathematical operation whose nature or effect is the opposite of another operation. For example, addition and subtraction are inverse operations, as are multiplication and division.
Noun
(ĭn'vûrs')
An inverse operation. Subtraction is the inverse of addition.
Either of a pair of elements in a set whose result under the mathematical operation of the set is the identity element. For example, the inverse of 5 under multiplication is 1/5 , since 5 × 1/5 = 1, the identity element under multiplication. The inverse of 5 under addition is -5, since 5 + -5 = 0.
inversemathematics Given a function, f : D -> C, a function g : C -> D is called a left inverse for f if for all d in D, g (f d) = d and a right inverse if, for all c in C, f (g c) = c and an inverse if both conditions hold. Only an injection has a left inverse, only a surjection has a right inverse and only a bijection has inverses. The inverse of f is often written as f with a -1 superscript. (1996-03-12)
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.
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.
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.
In*ver"sion\, n. [L. inversio: cf. F. inversion. See Invert.]1. The act of inverting, or turning over or backward, or the state of being inverted. 2. A change by inverted order; a reversed position or arrangement of things; transposition. It is just the inversion of an act of Parliament; your lordship first signed it, and then it was passed among the Lords and Commons. --Dryden. 3. (Mil.) A movement in tactics by which the order of companies in line is inverted, the right being on the left, the left on the right, and so on. 4. (Math.) A change in the order of the terms of a proportion, so that the second takes the place of the first, and the fourth of the third. 5. (Geom.) A peculiar method of transformation, in which a figure is replaced by its inverse figure. Propositions that are true for the original figure thus furnish new propositions that are true in the inverse figure. See Inverse figures, under Inverse. 6. (Gram.) A change of the usual order of words or phrases; as, "of all vices, impurity is one of the most detestable," instead of, "impurity is one of the most detestable of all vices." 7. (Rhet.) A method of reasoning in which the orator shows that arguments advanced by his adversary in opposition to him are really favorable to his cause. 8. (Mus.) (a) Said of intervals, when the lower tone is placed an octave higher, so that fifths become fourths, thirds sixths, etc. (b) Said of a chord, when one of its notes, other than its root, is made the bass. (c) Said of a subject, or phrase, when the intervals of which it consists are repeated in the contrary direction, rising instead of falling, or vice versa. (d) Said of double counterpoint, when an upper and a lower part change places. 9. (Geol.) The folding back of strata upon themselves, as by upheaval, in such a manner that the order of succession appears to be reversed. 10. (Chem.) The act or process by which cane sugar (sucrose), under the action of heat and acids or ferments (as diastase), is broken or split up into grape sugar (dextrose), and fruit sugar (levulose); also, less properly, the process by which starch is converted into grape sugar (dextrose). Note: The terms invert and inversion, in this sense, owe their meaning to the fact that the plane of polarization of light, which is rotated to the right by cane sugar, is turned toward the left by levulose.
Pro*por"tion\, n. [F., fr. L. proportio; pro before + portio part or share. See Portion.]1. The relation or adaptation of one portion to another, or to the whole, as respect magnitude, quantity, or degree; comparative relation; ratio; as, the proportion of the parts of a building, or of the body. The image of Christ, made after his own proportion. --Ridley. Formed in the best proportions of her sex. --Sir W. Scott. Documents are authentic and facts are true precisely in proportion to the support which they afford to his theory. --Macaulay. 2. Harmonic relation between parts, or between different things of the same kind; symmetrical arrangement or adjustment; symmetry; as, to be out of proportion. "Let us prophesy according to the proportion of faith." --Rom. xii. 6. 3. The portion one receives when a whole is distributed by a rule or principle; equal or proper share; lot. Let the women . . . do the same things in their proportions and capacities. --Jer. Taylor. 4. A part considered comparatively; a share. 5. (Math.) (a) The equality or similarity of ratios, especially of geometrical ratios; or a relation among quantities such that the quotient of the first divided by the second is equal to that of the third divided by the fourth; -- called also geometrical proportion, in distinction from arithmetical proportion, or that in which the difference of the first and second is equal to the difference of the third and fourth. Note: Proportion in the mathematical sense differs from ratio. Ratio is the relation of two quantities of the same kind, as the ratio of 5 to 10, or the ratio of 8 to 16. Proportion is the sameness or likeness of two such relations. Thus, 5 to 10 as 8 to 16; that is, 5 bears the same relation to 10 as 8 does to 16. Hence, such numbers are said to be in proportion. Proportion is expressed by symbols thus: a:b::c:d, or a:b = c:d, or a/b = c/d. (b) The rule of three, in arithmetic, in which the three given terms, together with the one sought, are proportional. Continued proportion, Inverse proportion, etc. See under Continued, Inverse, etc. Harmonical, or Musical, proportion, a relation of three or four quantities, such that the first is to the last as the difference between the first two is to the difference between the last two; thus, 2, 3, 6, are in harmonical proportion; for 2 is to 6 as 1 to 3. Thus, 24, 16, 12, 9, are harmonical, for 24:9::8:3. In proportion, according as; to the degree that. "In proportion as they are metaphysically true, they are morally and politically false." --Burke.
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Audio Help [adj., n. in-vurs, in-vurs; v. in-vurs] Pronunciation Key adjective, noun, verb, -versed, -vers·ing. 
