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The way an expression is written can depend on context. This is no different from your example of how spelling and grammar works in English. Two grammatically correct sentences can say the same thing in very different ways. Sums usually have their limits written above and below the summation sign, but space considerations might force the limits to the right. If the context is clear, sometimes the entire set to be summed over is written under the summation sign, with nothing above. There are rules for when you can do this, just like using "I" vs. "me" in English.töff said:I can't find a clear guide to mathematical notation. The best I found was a meager list of symbols. I even see sums being written with their limits to the right rather than above & below. Cripes! Do mathematicians even care about such concerns? I know, in the English language, there are precise rules for where commas go, how spaces get used (or not) with dashes & ellipses, yada yada. Are mathies just more laid back?
Yep, those rules are what I am looking for.Nimz said:... the entire set to be summed over is written under the summation sign, with nothing above. There are rules for when you can do this, just like using "I" vs. "me" in English
That's because there isn't a universal standard notation for evertyhing in mathematics. It's about clarity and context, that is all that matters.töff said:Normally I am an above-average web searcher.
But I cannot find any significant guide to mathematical notation.
(I should head over to the university library. I love that place.)
I find it hard to believe there's just NOT one out there!
I'm sure, but I have seen simmilar notation be used and parenthesis not added and it is just assumed the reader understands what is going on.Nimz said:Actually, something like
[tex] \sum_{k=0}^m \prod_{i=0}^n ki + n + \frac{3}{2} + j[/tex]
has a definite meaning, but it probably doesn't mean what is intended. As written, its meaning is the same as
[tex] \sum_{k=0}^m \left( \prod_{i=0}^n ki \right) + n + \frac{3}{2} + j[/tex].
Clarity is usually what counts the most, though, so the latter expression is definitely preferable.
Because I'm a writer. I want to write the math properly. I'm sorry if I have become annoying, but I did kinda assume that some other people might also care* about prescribed rules of notation and maybe be able to point me at them.0rthodontist said:Why do you care so much about this?
Where are those rules recorded?Nimz said:... the entire set to be summed over is written under the summation sign, with nothing above. There are rules for when you can do this, just like using "I" vs. "me" in English
That is a matter of rhetoric, which I grant is open to a lot of subjectivity, interpretation, and craftsmanship. However, there certainly are many hard and fast rules written down for grammar, spelling, and punctuation, in the field of language. Mathematics at the medial level (I ain't talking about the acroloci where math verges into philosophy) is a precise science. The notation you use is not open to interpretation. You have some latitude about how you describe & write an expression (my equation of sum-of-factorials = sum-of-products being an example!), but your notation system for writing that expression is as precise as the rules of grammar and punctuation that writers follow despite whatever rhetorical approaches they take.When would you use the word autodidact and when the phrase 'self taught'? ... there are no had and fast rules written down are there?
You'd be surprised who reads what. I mean, how do you think I wound up here? I ain't the only cross-discipline freak out there lurking in places I don't belong. Those freaks who lurk into writing & stylistics will find plenty of resources for understanding syntax, dialect, vocabulary, implication & connotation, capitalization, the Oxford Comma, use of single and double quotes, etc.etc. Those freaks (like me) who lurk into math, apparently, are S.double-O.L. for ready references, and are going to have to come in here and ask for help ... which, I suppose, amounts to word-of-mouth.If you don't know that then it's a fair bet that you wouldn't be reading a paper where it is assumed you do
töff said:The notation you use is not open to interpretation.
Yeh but apparently there is no list whatsoever, except the briefest of lists of what each symbol means, which is tantamount to a chart of the alphabet with the sounds each letter makes.There can be no exhaustive list
True! and the same applies to language, as portrayed wonderfully by George Orwell's "Newspeak" in 1984. That was a double-plus-good book!arildno said:An important thing to remember, is that it is damaging for your mental flexibility to be too dependent on unique, fixed symbolic notations for your concepts.
Evidently, you are still having the wrong focus on these matters.töff said:True! and the same applies to language, as portrayed wonderfully by George Orwell's "Newspeak" in 1984. That was a double-plus-good book!
Evidently. As enlightening as this all is, it is also frustrating.arildno said:Evidently, you are still having the wrong focus on these matters.
töff said:Where, for example, has anybody ever described how upper & lower limits can be specified or omitted/implied in sigma notation?
töff said:So as long as I get my meaning across, it doesn't matter how I spell and punctuate my formulae?
Oh God yes they have, from the Phoenicians through the Greeks and Hebrews, Shin to Sigma to S, all the Roman capitals, the Cyrillic alphabet, even the Cherokee syllabary ... there are histories of western writing systems, books about typefaces and letterforms, calligraphy manuals, analyses of medieval illuminated manuscripts, auctions for old lead or wooden typesetting blocks ... good lord, you could make a career of the letter "S" up to and including Superman's cape.matt grime said:I'm reasonably sure no one has seen fit to catalogue every single possible way to draw the letter s, either.
töff said:Oh God yes they have, from the Phoenicians through the Greeks and Hebrews, Shin to Sigma to S, all the Roman capitals, the Cyrillic alphabet, even the Cherokee syllabary ... there are histories of western writing systems, books about typefaces and letterforms, calligraphy manuals, analyses of medieval illuminated manuscripts, auctions for old lead or wooden typesetting blocks ... good lord, you could make a career of the letter "S" up to and including Superman's cape.