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| Understanding a definition in mathematics is a pretty complicated and laborious process. The following table summarizes some of the things one might do when trying to understand a new definition.
| | #redirect [[learning:Understanding mathematical definitions]] |
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| {| class="sortable wikitable"
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| ! Step !! Condition !! Description !! Purpose !! Example
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| | Type-checking and parsing ||
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| | Checking assumptions of objects introduced || || Remove or alter each assumption of the objects that have been introduced in the definition to see why they are necessary.
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| | Come up with examples ||
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| | Come up with counterexamples ||
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| | Writing out a wrong version of the definition || || || || See [https://gowers.wordpress.com/2011/09/30/basic-logic-quantifiers/ this post] by Tim Gowers (search "wrong versions" on the page).
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| | Understand the kind of definition || || Generally a definition will do one of the following things: (1) it will construct a brand new type of object (e.g. definition of a ''function''); (2) it will take an existing type of object and create a predicate to describe some subclass of that type of object (e.g. take the integers and create the predicate ''even''); (3) it will define an operation on some class of objects (e.g. take integers and define the operation of ''addition'').
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| | Check that it is well-defined || If the definition defines an operations ||
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| | Check it is consistent with the old one || If the definition supersedes an older definition or it clobbers up a previously defined notation ||
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| | Disambiguate similar-seeming concepts ||
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| |}
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| ==See also==
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| * [[Understanding theorems]]
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| ==External links==
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| * https://www.maa.org/node/121566 lists some other steps for both theorems and definitions
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