Definitions for bounded function
bound·ed func·tion

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1. bounded functionnoun

   Any function whose values remain bounded by some constant.

WikipediaRate this definition:0.0 / 0 votes

1. Bounded function

   In mathematics, a function f defined on some set X with real or complex values is called bounded if the set of its values is bounded. In other words, there exists a real number M such that | f ( x ) | ≤ M {\displaystyle |f(x)|\leq M} for all x in X. A function that is not bounded is said to be unbounded.If f is real-valued and f(x) ≤ A for all x in X, then the function is said to be bounded (from) above by A. If f(x) ≥ B for all x in X, then the function is said to be bounded (from) below by B. A real-valued function is bounded if and only if it is bounded from above and below.An important special case is a bounded sequence, where X is taken to be the set N of natural numbers. Thus a sequence f = (a0, a1, a2, ...) is bounded if there exists a real number M such that | a n | ≤ M {\displaystyle |a_{n}|\leq M} for every natural number n. The set of all bounded sequences forms the sequence space l ∞ {\displaystyle l^{\infty }} .The definition of boundedness can be generalized to functions f : X → Y taking values in a more general space Y by requiring that the image f(X) is a bounded set in Y.

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1. Bounded function

   In mathematics, a function f defined on some set X with real or complex values is called bounded, if the set of its values is bounded. In other words, there exists a real number M such that for all x in X. Sometimes, if f(x) ≤ A for all x in X, then the function is said to be bounded above by A. On the other hand, if f(x) ≥ B for all x in X, then the function is said to be bounded below by B. The concept should not be confused with that of a bounded operator. An important special case is a bounded sequence, where X is taken to be the set N of natural numbers. Thus a sequence f = is bounded if there exists a real number M such that for every natural number n. The set of all bounded sequences, equipped with a vector space structure, forms a sequence space. This definition can be extended to functions taking values in a metric space Y. Such a function f defined on some set X is called bounded if for some a in Y there exists a real number M such that its distance function d is less than M, i.e. for all x in X. If this is the case, there is also such an M for each other a, by the triangle inequality.

How to pronounce bounded function?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

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   Fred

   US English

   Tessa

   South African

How to say bounded function in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of bounded function in Chaldean Numerology is: 9

2. Pythagorean Numerology

   The numerical value of bounded function in Pythagorean Numerology is: 5

References

1. ^ Wiktionary
   https://en.wiktionary.org/wiki/Bounded_Function
2. ^ Wikipedia
   https://en.wikipedia.org/wiki/Bounded_Function
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=bounded function