User talk:David Eppstein/2018b

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Notation for definite integrals

Hello, David. I have just seen this edit at Series (mathematics), where in your edit summary you said "you can't have an already-bound variable as the variable of integration". Certainly there are many situations where using the same letter to represent both the bound variable of integration and a limit of integration is undesirable, but it is certainly logically possible, and in some contexts useful, to use a letter to represent a bound variable which and the same letter to represent another variable outside the scope of that bound variable. This is exactly the same principal as using the same textual name for a local and a global variable in computer programming. (Or more as local variable and another variable, local or global, whose scope excludes that of the first variable.)

I am posting these comments essentially in case you may find it of some interest, rather than to criticise your edit, but I do also think there is a good case for regarding the edit in question as being one of the contexts in which it is better to use the same variable. The variable t is not used in any way other than as a dummy variable to satisfy the notational convention of always having a letter to represent the variable of integration, so any arbitrary letter will do as such a dummy, and using the same letter as is used in a different scope will not cause any ambiguity or difficulty in understanding. Anyone with only an elementary knowledge of calculus is likely to be used to consistently using two letters (usually x and y) to represent the variables in each of two dimensions, not switching letters between bound and unbound uses of a variable in the same dimension. They will therefore understand the notation using x in both places without difficulty, but may be confused by the version which introduces another letter which they may not understand the purpose of. On the other hand anyone with more than such an elementary knowledge will have no difficulty understanding it: they will either regard it as a perfectly valid use of the same symbol in two non-overlapping scopes, or at worst they will regard it as an "abuse of notation" but perfectly comprehensible, so either way nothing will be lost. The editor who uses the pseudonym "JamesBWatson" (talk) 10:27, 3 April 2018 (UTC)

I think those two cases should be differentiated. EEng 13:39, 3 April 2018 (UTC) P.S. to DE: Thanks for being available on Sunday. Predictions of apocalypse were unfounded.
Programming languages have explicit rules for scoping and shadowing of variables when you use the same name more than once. Mathematics usually just disallows the repetition. In any case I think it's bad style and confusing to do this. —David Eppstein (talk) 15:56, 3 April 2018 (UTC)
Seriously now, I agree. EEng 18:14, 3 April 2018 (UTC)

DYK for Prime number

On 4 April 2018, Did you know was updated with a fact from the article Prime number, which you recently created, substantially expanded, or brought to good article status. The fact was ... that prime numbers have been studied since the time of the ancient Greeks, but have had few real-world applications until the invention of public-key cryptography in the 1970s? The nomination discussion and review may be seen at Template:Did you know nominations/Prime number. You are welcome to check how many page hits the article got while on the front page (here's how, Prime number), and it may be added to the statistics page if the total is over 5,000. Finally, if you know of an interesting fact from another recently created article, then please feel free to suggest it on the Did you know talk page.

Alex Shih (talk) 00:02, 4 April 2018 (UTC)

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