nLab
denial inequality
Context
Relations
Equality and Equivalence
equivalence

equality (definitional , propositional , computational , judgemental , extensional , intensional , decidable )

identity type , equivalence in homotopy type theory

isomorphism , weak equivalence , homotopy equivalence , weak homotopy equivalence , equivalence in an (∞,1)-category

natural equivalence , natural isomorphism

gauge equivalence

Examples.

principle of equivalence

equation

fiber product , pullback

homotopy pullback

Examples.

linear equation , differential equation , ordinary differential equation , critical locus

Euler-Lagrange equation , Einstein equation , wave equation

Schrödinger equation , Knizhnik-Zamolodchikov equation , Maurer-Cartan equation , quantum master equation , Euler-Arnold equation , Fuchsian equation , Fokker-Planck equation , Lax equation

Foundations
foundations

The basis of it all Foundational axioms

basic constructions:

:

:

:

strong axioms

further

Removing axioms
The denial inequality is the negation of equality .

This is a term found in constructive mathematics , to distinguish from other inequality relations such as apartness . It is taken for granted in classical mathematics .

If one wishes to reserve the word “inequality” for order relations (such as $\le$ and $\lt$ ), then one may instead use the word disequality to refer to the denial inequality. (For instance, this is common in type theory with subtype relations that form an ordering on the types.)

Last revised on June 25, 2013 at 06:50:38.
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