Help:Multiple Definitions

Different sources may give different Definitions for the same thing. Because aims to be accessible to a large public, equivalent definitions are treated equally.

Introduction
Instead of choosing only one definition as the "main" definition and taking the other definitions as theorems, on equivalent definitions are bundled on the same definition page. Their equivalence is proved on a separate page. This has multiple advantages:


 * Every student feels at home at, regardless of the definition their textbook uses.
 * Seeing different definitions in one glance, increases the chance for a visitor to understand the concept being defined.
 * Different viewpoints on the same concept makes more coherent, without making the pages appear too encyclopaedic.

Page Structure
The structure of page with multiple equivalent definitions is roughly as follows:

Definition
Let ... ... Let ...

Second transcluded definition
...

Also see

 * Equivalence of Definitions of Concept that is Defined

As with multiple proofs, the introductory part is copied identically on the transcluded subpages, but not inside the  tags.

A link to a proof showing their equivalence (see below) is placed in the Also see section.

Equivalence Proofs
The equivalence of the definitions has to be proved on a separate page. More instructions at Help:Definition Equivalences.

Generalizations

 * See also Help:Accessibility

Nonequivalent definitions

 * See also Help:Also defined as

Also see

 * Help:Multiple Proofs