User:Contribution/Limit: Difference between revisions

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See [[User:Contribution/Minimal_Prime_Limit|minimal prime limit]]

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

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==

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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.

~~In other words, 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-factor-limit, called the '''~~minimal factor limit~~''', for a given positive integer fmin if and only if the sum of the exponent absolutes of its factorization into primes is more than or equal to fmin.~~

See [[User:Contribution/Factor_Limit#Minimal_factor_limit|minimal factor limit]]

~~In other words, a~~ positive rational number q belongs to the fmin-limit if and only if the sum of the exponent absolutes of its factorization into primes is left-bounded to fmin.

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-factor-limit, called the '''~~maximal factor limit~~''', for a given positive integer fmax if and only if the sum of the exponent absolutes of its factorization into primes is less than or equal to fmax.~~

See [[User:Contribution/Factor_Limit#Maximal_factor_limit|maximal factor limit]]

~~In other words, a~~ positive rational number q belongs to the fmax-limit if and only if the sum of the exponent absolutes of its factorization into primes is right-bounded to fmax.

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.

@@ Line 9: / Line 9: @@
 See [[User:Contribution/Minimal_Prime_Limit|minimal prime limit]]
-A positive rational number q belongs to the pmin-limit if and only if all primes of its factorization into primes are left-bounded to pmin.
+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==
@@ Line 15: / Line 15: @@
 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.
-In other words, 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-factor-limit, called the '''minimal factor limit''', for a given positive integer fmin if and only if the sum of the exponent absolutes of its factorization into primes is more than or equal to fmin.
+See [[User:Contribution/Factor_Limit#Minimal_factor_limit|minimal factor limit]]
-In other words, a positive rational number q belongs to the fmin-limit if and only if the sum of the exponent absolutes of its factorization into primes is left-bounded to fmin.
+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-factor-limit, called the '''maximal factor limit''', for a given positive integer fmax if and only if the sum of the exponent absolutes of its factorization into primes is less than or equal to fmax.
+See [[User:Contribution/Factor_Limit#Maximal_factor_limit|maximal factor limit]]
-In other words, a positive rational number q belongs to the fmax-limit if and only if the sum of the exponent absolutes of its factorization into primes is right-bounded to fmax.
+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.