PositiveIntegers
represents the domain of strictly positive integers, as in x∈PositiveIntegers.
Details
- x∈PositiveIntegers evaluates immediately if x is a numeric quantity.
- Simplify[expr∈PositiveIntegers,assum] can be used to try to determine whether an expression is a positive integer under the given assumptions.
- (x1x2…)∈PositiveIntegers and {x1,x2,…}∈PositiveIntegers test whether all xi are positive integers.
- PositiveIntegers is output in StandardForm or TraditionalForm as
![TemplateBox[{}, PositiveIntegers]](Files/PositiveIntegers.en/1.png "TemplateBox[{}, PositiveIntegers]")
. This typeset form can be input using 
pints
.
Examples
open all close allBasic Examples (3)
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:
TraditionalForm formatting:
Applications (1)
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:
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