# User:Contribution/Limit

## Contents

#### 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

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

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

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.