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| ==Minimal prime limit== | | ==Minimal prime limit== |
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| A positive rational number q belongs to the pmin-limit, called the '''minimal prime limit''', for a given prime number pmin if and only if it can be factored into primes (with positive or negative integer exponents) of size more than or equal to pmin.
| | See [[User:Contribution/Minimal_Prime_Limit|minimal prime limit]] |
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| In other words, 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. |
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| ==Maximal prime limit== | | ==Maximal prime limit== |
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| Also called [[harmonic limit]]. | | Also called [[harmonic limit]]. |
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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-max-prime-limit if and only if all primes of its factorization into primes are right-bounded to pmax. |
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| 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.
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| ==Minimal factor limit== | | ==Minimal factor limit== |
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| 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]] |
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| 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. |
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| ==Maximal factor limit== | | ==Maximal factor limit== |
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| 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]] |
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| 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. |