User:Contribution/Limit: Difference between revisions
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====Purpose==== | ====Purpose==== | ||
An [[harmonic limit]] is a set of rational numbers whose the prime numbers into its prime factorization are right-bounded. | 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 rational number limiting subsets. | The goal of this page is to list several kinds of positive rational number limiting subsets. | ||
==Minimal prime limit== | ==Minimal prime limit== | ||
See [[User:Contribution/Minimal_Prime_Limit|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== | ==Maximal prime limit== | ||
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Also called [[harmonic limit]]. | Also called [[harmonic limit]]. | ||
A positive rational number q belongs to the 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. | ||
==Minimal factor limit== | ==Minimal factor limit== | ||
See [[User:Contribution/Factor_Limit#Minimal_factor_limit|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== | ==Maximal factor limit== | ||
See [[User:Contribution/Factor_Limit#Maximal_factor_limit|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. | |||
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
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.