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by riazrizvi
2157 days ago
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Unambiguity as an adjective is slippery. Mathematical notation must be concise, because a key purpose is to provide understanding, which it achieves by focused abstraction. So when you search for notation to model some real world system, you leave things out, as such it leaves room for interpretation when remapping back to the real world, ie there is ambiguity. I think this #1 item should really be termed Consistency, because above all, notation must not contradict itself. |
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This is a good goal, but I'm not sure it's the primary goal; the phrase 'abuse of notation' exists precisely to describe its breakage, with even the best mathematicians and expositors engaging in it, and I think insisting on no abuse of notation leads us rapidly to the style of impenetrable Principia-style logic, or of modern formal proofs—both of which have their place (at least the latter …), but neither of which should govern all mathematical discourse.
As with all writing, I think that part of being a good mathematical writer is knowing the rules so that you can figure out when to break them unintentionally, rather than stumbling into it accidentally.