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 | Condition | 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 | 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). | |||
| Check that it is well-defined | If the definition defines an operations | |||
| Check it is consistent with the old one | If the definition supersedes an older definition |