User:IssaRice/Understanding definitions: Difference between revisions
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! Step !! Description !! Purpose !! Example | ! Step !! Condition !! Description !! Purpose !! Example | ||
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| Type-checking and parsing || | | 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. | | 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 || | | Come up with examples || | ||
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| Understand the kind of definition || | | Understand the kind of definition || | ||
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| If the definition defines an operations | | Check that it is well-defined || If the definition defines an operations || | ||
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| If the definition supersedes an older definition | | Check it is consistent with the old one || If the definition supersedes an older definition || | ||
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Revision as of 21:08, 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 | 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 | ||||
| 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 |