User:IssaRice/Understanding definitions: Difference between revisions
No edit summary |
No edit summary |
||
| Line 21: | Line 21: | ||
| If the definition supersedes an older definition, check it is consistent with the old one || | | If the definition supersedes an older definition, check it is consistent with the old one || | ||
|} | |} | ||
==See also== | |||
* [[Understanding theorems]] | |||
Revision as of 21:07, 3 December 2018
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.
| Step | Description | Purpose | Example |
|---|---|---|---|
| Type-checking and parsing | |||
| 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. | ||
| Come up with examples | |||
| Come up with counterexamples | |||
| Writing out a wrong version of the definition | |||
| Understand the kind of definition | |||
| If the definition defines an operations, check that it is well-defined | |||
| If the definition supersedes an older definition, check it is consistent with the old one |