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Integral part

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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.

where the product consists of all primes not exceeding , and

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

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
This article was adapted from an original article by B.M. Bredikhin (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article