User:IssaRice/Understanding definitions

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