| Abuse Of Notation |
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| mathematical notation | |
| mathematical terminology | |
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Common examples occur when speaking of compound mathematical objects. For example, a Topological Space consists of a set and a topology , and two topological spaces and can be quite different if they have different topologies. Nevertheless, it is common to refer to such a space simply as when there is no danger of confusion or when it is implicitly clear what topology is being considered. Similarly, one often refers to a Group as simply when the group operation is clear from context. ADVANTAGES The new use may achieve clarity in the new area in an unexpected way. DISADVANTAGES The new use may borrow arguments from the old area that do not carry over, creating a False Analogy . EXAMPLES John Harrison cites "the use of ''f''(''x'') to represent both application of a function ''f'' to an argument ''x'', and the image under ''f'' of a subset, ''x'', of f's domain". QUOTATION :"We will occasionally use this arrow notation unless there is no danger of confusion." ( Ronald L. Graham , ''Rudiments of Ramsey Theory '') SEE ALSO EXTERNAL LINKS
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