IsOdd

Whether n is an odd integer.

✓ checked against that system · ! checked, with disagreements (hover a chip)Fungrim entry1c3766↗28b4c3↗64f0a5↗c0e088✓↗fd732d✓↗Wolfram LanguageOddQ!↗

IsOdd(n)$True$ if $n$ is an odd integer, else $False$.

Juliais_odd(ZZ(n))Rustis_odd(n)

Typed signatures

Type	Package	Applies
(number) -> boolean	analyticreplaces compute-engine	always
(number) -> boolean	compute-engine	always

Domain: Arithmetic

Examples

Basic #

live ↗

In$\mathrm{IsOdd}(3)$Out$\mathrm{True}$

live ↗

In$\mathrm{IsOdd}(4)$Out$\mathrm{False}$

Negative integers count too

live ↗

In$\mathrm{IsOdd}(-7)$Out$\mathrm{True}$

live ↗

In$\mathrm{IsOdd}(0)$Out$\mathrm{False}$

9 is odd

live ↗

In$\mathrm{IsOdd}(9)$Out$\mathrm{True}$

Scope #

A non-integer is not odd

live ↗

In$\mathrm{IsOdd}(3.5)$Out$\mathrm{False}$

live ↗

In$\mathrm{IsOdd}(\frac{1}{3})$Out$\mathrm{False}$

Big integers

live ↗

In$\mathrm{IsOdd}(2^{100}+1)$Out$\mathrm{True}$

$\pi$ is known not to be an integer, so it is decided False

live ↗

In$\mathrm{IsOdd}(π)$Out$\mathrm{False}$

Threads element-wise over a list

live ↗

In$\mathrm{IsOdd}(\bigl\lbrack1, 2, 3\bigr\rbrack)$Out$\bigl\lbrack\mathrm{True}, \mathrm{False}, \mathrm{True}\bigr\rbrack$

Applications #

Select the odd numbers up to 10

live ↗

In$\mathrm{Filter}(1..10, \mathrm{IsOdd})$Out$\bigl\lbrack1, 3, 5, 7, 9\bigr\rbrack$

True if every entry is odd

live ↗

In$\mathrm{IsVector}(\bigl\lbrack1, 5, 7, 11\bigr\rbrack, \mathrm{IsOdd})$Out$\mathrm{True}$

False because the first entry is even

live ↗

In$\mathrm{IsVector}(\bigl\lbrack2, 5, 7, 11\bigr\rbrack, \mathrm{IsOdd})$Out$\mathrm{False}$

Properties #

An integer is odd exactly when it is not even. See IsEven

live ↗

In$\mathrm{IsOdd}(7)=¬\mathrm{IsEven}(7)$Out$\mathrm{True}$

2 is even, hence not odd

live ↗

In$\mathrm{IsOdd}(2)$Out$\mathrm{False}$

15 is odd

live ↗

In$\mathrm{IsOdd}(15)$Out$\mathrm{True}$

Possible issues #

A symbol stays undecided rather than False

live ↗

In$\mathrm{IsOdd}(x)$Out$\mathrm{IsOdd}(x)$

About

Examples	17
Checked against	Wolfram Language 16 agree1 differSymPy 13 agree1 differJulia 9 agree3 errorRust 9 agree3 error
Crosswalk	Fungrim entry ×5Wolfram LanguageJuliaRust

Implementation

mappedsympypackages/oracle/src/mappings.ts

Wolfram's OddQ is False unless the operand is an odd integer, so SymPy's undecided is_odd (None), as for a symbol or 4.0, reads as False.

mappedjuliapackages/oracle/src/mappings.ts

mappedrustpackages/oracle/src/mappings.ts

See also: IsEven