# PositiveIntegers

represents the domain of strictly positive integers, as in xPositiveIntegers.

# Details

• xPositiveIntegers evaluates immediately if x is a numeric quantity.
• Simplify[exprPositiveIntegers,assum] can be used to try to determine whether an expression is a positive integer under the given assumptions.
• (x1|x2|)PositiveIntegers and {x1,x2,}PositiveIntegers test whether all xi are positive integers.
• PositiveIntegers is output in StandardForm or TraditionalForm as . This typeset form can be input using pints.

# Examples

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## Basic Examples(3)

Seven is a positive integer:

If is an integer, then is a positive integer:

Find positive integer solutions of a Pell equation:

## Scope(6)

Test domain membership of a numeric expression:

Make domain membership assumptions:

Specify the default domain over which a function should work:

Solve an optimization problem over the positive integers:

Test whether several numbers are positive integers:

If any number is explicitly not a positive integer, the result is False:

## Applications(1)

Testing membership in the positive integers is a fast way to verify positivity of a large list of integers:

## Properties & Relations(3)

Membership in PositiveIntegers is equivalent to membership in Integers along with positivity:

PositiveIntegers is contained in PositiveReals and PositiveRationals:

PositiveIntegers is disjoint from NonPositiveIntegers and NegativeIntegers:

Wolfram Research (2019), PositiveIntegers, Wolfram Language function, https://reference.wolfram.com/language/ref/PositiveIntegers.html.

#### Text

Wolfram Research (2019), PositiveIntegers, Wolfram Language function, https://reference.wolfram.com/language/ref/PositiveIntegers.html.

#### CMS

Wolfram Language. 2019. "PositiveIntegers." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/PositiveIntegers.html.

#### APA

Wolfram Language. (2019). PositiveIntegers. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PositiveIntegers.html

#### BibTeX

@misc{reference.wolfram_2024_positiveintegers, author="Wolfram Research", title="{PositiveIntegers}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/PositiveIntegers.html}", note=[Accessed: 21-June-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_positiveintegers, organization={Wolfram Research}, title={PositiveIntegers}, year={2019}, url={https://reference.wolfram.com/language/ref/PositiveIntegers.html}, note=[Accessed: 21-June-2024 ]}