Integral part
From Encyclopedia of Mathematics
entier, integer part of a (real) number
The largest integer not exceeding . It is denoted by
or by
. It follows from the definition of an integer part that
. If
is an integer,
. Examples:
;
,
. The integral part is used in the factorization of, for example, the number
, viz.
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where the product consists of all primes not exceeding
, and
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The function of the variable
is piecewise continuous (a step function) with jumps at the integers. Using the integral part one defines the fractional part of a number
, denoted by the symbol
and given by
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The function is a periodic and piecewise continuous.
References
[1] | I.M. Vinogradov, "Elements of number theory" , Dover, reprint (1954) (Translated from Russian) |
How to Cite This Entry:
Integral part. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Integral_part&oldid=33155
Integral part. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Integral_part&oldid=33155
This article was adapted from an original article by B.M. Bredikhin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article