Difference between revisions of "Examples in mathematics"

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(Unit testing and examples)
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==Unit testing and examples==
 
==Unit testing and examples==
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{| class="wikitable"
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|-
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!
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! Is an example according to definition
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! Is not an example according to definition
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|-
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! Is an example according to intuition
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| An "obvious" example, or central example.
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| A surprising non-example.
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|-
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! Is not an example according to intuition
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| A surprising example.
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| An obvious non-example.
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|}
  
 
==Hierarchical nature of examples==
 
==Hierarchical nature of examples==

Revision as of 02:06, 19 February 2019

Examples in mathematics have different flavor than examples in other disciplines. This is probably because definitions in mathematics are different from definitions in other disciplines (mathematical definitions are exact). Some common problems of deciding whether something is or is not an example do not appear in mathematics. Instead, there are other problems.

Unit testing and examples

Is an example according to definition Is not an example according to definition
Is an example according to intuition An "obvious" example, or central example. A surprising non-example.
Is not an example according to intuition A surprising example. An obvious non-example.

Hierarchical nature of examples

Something can be considered "concrete" or "abstract" depending on the context. Consider a term like "metric space". One can give examples of metric spaces. On the other hand, a metric space is itself an example (of a structured space, of a topological space).