Template:Lemma

This is the 'Lemma' template. It should be called in the following format:

Edit the page to see the template text.

The following pages define the word :

About Words and Definitions
There are (at least!) two practical problems, in organizing a lexicon of mathematical words. One is the problem of disambiguation, and the other is a problem of perspective.

An example of disambiguation is given by the mathematical noun "domain". When talking about functions, one refers to the "domain of a function". When talking about commutative rings, one refers to a "domain", i.e., an "integral domain". These are completely different meanings for the same word. In such cases, there are two pages in the Lexicon -- one for each meaning.

The problem of perspective is that one word, like "continuous" has various but mathematically compatible meanings, in different contexts. For a student of topology, continuity often refers to the fact that the preimage of an open set is open. For a student of calculus, continuity often refers to an "epsilon-delta" definition. These definitions are certainly compatible, but different definitions should be given for different audiences. In such situations, only one word is listed in the Lexicon, but many pages may define the word.