Increasing function

Increasing function
Increase In*crease", v. i. [imp. & p. p. {Increased}; p. pr. & vb. n. {Increasing}.] [OE. incresen, encresen, enrescen, OF. encreistre, fr. L. increscere; pref. in- in + crescere to grow. See {Crescent}, and cf. {Decrease}.] [1913 Webster] 1. To become greater or more in size, quantity, number, degree, value, intensity, power, authority, reputation, wealth; to grow; to augment; to advance; -- opposed to {decrease}. [1913 Webster]

The waters increased and bare up the ark. --Gen. vii. 17. [1913 Webster]

He must increase, but I must decrease. --John iii. 30. [1913 Webster]

The heavens forbid But that our loves and comforts should increase, Even as our days do grow! --Shak. [1913 Webster]

2. To multiply by the production of young; to be fertile, fruitful, or prolific. [1913 Webster]

Fishes are more numerous or increasing than beasts or birds, as appears by their numerous spawn. --Sir M. Hale. [1913 Webster]

3. (Astron.) To become more nearly full; to show more of the surface; to wax; as, the moon increases. [1913 Webster]

{Increasing function} (Math.), a function whose value increases when that of the variable increases, and decreases when the latter is diminished; also called a {monotonically increasing function}.

Syn: To enlarge; extend; multiply; expand; develop; heighten; amplify; raise; enhance; spread; aggravate; magnify; augment; advance.

Usage: To {Increase}, {Enlarge}, {Extend}. Enlarge implies to make larger or broader in size. Extend marks the progress of enlargement so as to have wider boundaries. Increase denotes enlargement by growth and internal vitality, as in the case of plants. A kingdom is enlarged by the addition of new territories; the mind is enlarged by knowledge. A kingdom is extended when its boundaries are carried to a greater distance from the center. A man's riches, honors, knowledge, etc., are increased by accessions which are made from time to time. [1913 Webster]


The Collaborative International Dictionary of English. 2000.

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  • increasing function — noun Any function of a real variable whose value increases (or is constant) as the variable increases …   Wiktionary

  • increasing function — noun : a mathematical function whose value algebraically increases as the independent variable algebraically increases over a given range …   Useful english dictionary

  • monotonically increasing function — Increase In*crease , v. i. [imp. & p. p. {Increased}; p. pr. & vb. n. {Increasing}.] [OE. incresen, encresen, enrescen, OF. encreistre, fr. L. increscere; pref. in in + crescere to grow. See {Crescent}, and cf. {Decrease}.] [1913 Webster] 1. To… …   The Collaborative International Dictionary of English

  • strictly increasing function — Math. a function having the property that for any two points in the domain such that one is larger than the other, the image of the larger point is greater than the image of the smaller point. Cf. strictly decreasing function. * * * …   Universalium

  • strictly increasing function — Math. a function having the property that for any two points in the domain such that one is larger than the other, the image of the larger point is greater than the image of the smaller point. Cf. strictly decreasing function …   Useful english dictionary

  • strictly increasing function — noun Any function of a real variable who value increases as the variable increases …   Wiktionary

  • Increasing — Increase In*crease , v. i. [imp. & p. p. {Increased}; p. pr. & vb. n. {Increasing}.] [OE. incresen, encresen, enrescen, OF. encreistre, fr. L. increscere; pref. in in + crescere to grow. See {Crescent}, and cf. {Decrease}.] [1913 Webster] 1. To… …   The Collaborative International Dictionary of English

  • Function overloading — or method overloading is a feature found in various programming languages such as Ada, C#, VB.NET, C++, D and Java that allows the creation of several methods with the same name which differ from each other in terms of the type of the input and… …   Wikipedia

  • increasing monotonic — adjective consistently increasing an increasing monotonic function • Similar to: ↑monotonic, ↑monotone …   Useful english dictionary

  • function — Fluent Flu ent, n. 1. A current of water; a stream. [Obs.] [1913 Webster] 2. [Cf. F. fluente.] (Math.) A variable quantity, considered as increasing or diminishing; called, in the modern calculus, the {function} or {integral}. [1913 Webster] …   The Collaborative International Dictionary of English

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