NotEqual

Generated from the engine's own definition: compute-engine's symbol, which we neither extend nor document by hand.

Inequality comparison (not equal to).

✓ checked against that system · ! checked, with disagreements (hover a chip)WikipediaInequality (mathematics)↗MathWorldInequality↗WikidataQ28113351↗Encyclopedia of MathematicsInequality↗Britannicatopic/inequality↗DLMF1.7↗FungrimNotEqual↗Wolfram LanguageUnequal✓↗

NotEqual(any, any) -> booleanInequality comparison (not equal to).

Typed signatures

Type	Package	Applies
(any, any) -> boolean	residuesreplaces compute-engine	on IntegerMod
(any, any*) -> boolean	adelesreplaces compute-engine	on Adele, Idele, ProfiniteNumber
(any, any*) -> boolean	compute-engine	always

Domain: Compute engine

Examples

1 more kept as data, checked against the oracles

Basic #

Distinct integers are unequal

live ↗

In$1≠2$Out$\mathrm{True}$

Scope #

Exact rationals are compared exactly

live ↗

In$\frac{3}{2}≠\frac{5}{3}$Out$\mathrm{True}$

Inequalities combine with logical And

live ↗

In$3≠4∧4≠5$Out$\mathrm{True}$

Strings compare case-sensitively

live ↗

In$\text{abc}≠\text{ABC}$Out$\mathrm{True}$

live ↗

In$π^{e}≠e^{π}$Out$\mathrm{True}$

live ↗

In$\bigl\lbrack a, b, c\bigr\rbrack≠\bigl\lbrack d, k\bigr\rbrack$Out$\mathrm{True}$

live ↗

In$1≠1+128×(10^{-16})$Out$\mathrm{True}$

live ↗

In$1≠1+256×(10^{-16})$Out$\mathrm{True}$

Properties #

Decides what it can: $\sqrt2 + \sqrt3 = \sqrt{5 + 2\sqrt6}$; $x \ne y$ stays open

live ↗

In$\begin{cases}x≠x\\x≠y\\\sqrt{2}+\sqrt{3}≠\sqrt{5+2\sqrt{6}}\\π≠N(π)\end{cases}$Out$\bigl\lbrack\mathrm{False}, x≠y, \mathrm{False}, \mathrm{False}\bigr\rbrack$

About

Examples	10
Checked against	Wolfram Language 9 agreempmath 5 agree1 differ1 error
Crosswalk	WikipediaMathWorldWikidataEncyclopedia of MathematicsBritannicaDLMFFungrimWolfram Language

Implementation

mappedmpmathpackages/oracle/src/mappings.ts