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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-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-limit if and only if all primes of its factorization into primes are right-bounded to pmax. | |||
==Minimal factor limit== | ==Minimal factor limit== | ||
Revision as of 18:28, 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
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-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-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.