User:Contribution/Limit: Difference between revisions

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Also called [[harmonic limit]].
Also called [[harmonic limit]].


A positive rational number q belongs to the pmax-limit, called the '''maximal prime limit''', for a given prime number pmax if and only if it can be factored into primes (with positive or negative integer exponents) of size less than or equal to pmax.
A positive rational number q belongs to the pmax-max-prime-limit if and only if all primes of its factorization into primes are right-bounded to pmax.
 
A positive rational number q belongs to the pmax-limit if and only if all primes of its factorization into primes are right-bounded to pmax.


==Minimal factor limit==
==Minimal factor limit==

Latest revision as of 18:29, 16 June 2020

Purpose

An harmonic limit is a set of positive rational numbers whose the prime numbers into its prime factorization are right-bounded.

The goal of this page is to list several kinds of positive rational number limiting subsets.

Minimal prime limit

See minimal prime limit

A positive rational number q belongs to the pmin-min-prime-limit if and only if all primes of its factorization into primes are left-bounded to pmin.

Maximal prime limit

Also called harmonic limit.

A positive rational number q belongs to the pmax-max-prime-limit if and only if all primes of its factorization into primes are right-bounded to pmax.

Minimal factor limit

See minimal factor limit

A positive rational number q belongs to the fmin-min-factor-limit if and only if the sum of the exponent absolutes of its factorization into primes is left-bounded to fmin.

Maximal factor limit

See maximal factor limit

A positive rational number q belongs to the fmax-max-factor-limit if and only if the sum of the exponent absolutes of its factorization into primes is right-bounded to fmax.