It seems to me that "so" is seldom used in math proofs. Instead, "hence" and "therefore" are used very often, even repeatedly appearing in several sentences in a row. So I wonder if my feeling is correct? What do you think is proper use of these words or similar ones in math proofs? Thanks!
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3So, you don't agree with those pedants who insist not to begin a sentence with So.– KrisOct 25, 2012 at 4:01
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1@Kris: I agree that sentences should not begin with "and", but as far as I know beginning with "so" is okay/fine.– TimOct 25, 2012 at 11:40
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1@Kris: I've no objection to your starting a sentence with "so" there, since it "obliquely references" Tim's question. What I find lamentable is the number of OP's who start their question text with "So". Doubtless some people just think "So what?", but it really does strike me as an ignorant way to open a dialogue.– FumbleFingersOct 25, 2012 at 12:19
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1I always avoided using "so" in proofs when studying maths, because it could be too easily confused with "50".– UrbycozOct 25, 2012 at 13:13
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2 Answers
The computer scientist Donald Knuth, who is essentially a mathematician, has written quite a lot about how to write mathematics in a clear and intelligible style. In his book, "Mathematical Writing", co-authored with Tracy Larrabee and Paul Roberts, Knuth uses the word "so" quite a lot. In 118 pages of text, "So ..." (i.e., as the opening word of a sentence) appears 26 times. I think that one of his best pieces of advice is, "Don't get hung up on one or two styles of sentences." At other places in the book he seems to press the idea that good mathematical writing has both consistency (so that the same concept does not appear, ambiguously, as if it were some other concept) and variety of expression.
Of course, none of this specifically addresses your comment about the appearance of the word "so" in proofs, but it does give an idea of the way a person who is a clear expositor of mathematics uses it.
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The use of so as the opening word of a sentence is one thing and So as part of a formal proof of theorem is quite another. Which may actually be another reason we should avoid it there.– KrisOct 25, 2012 at 12:05
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Btw, I find your reference interesting, any online links possibly? Reviews/ extracts even?– KrisOct 25, 2012 at 12:06
There is a school of thought that a sentence may not begin with So. Therefore, it is seldom so in formal writing.
Hence and therefore may be considered synonyms, or at least interchangeable.
I suspect that hence is preferred where the inference derives from the immediately preceding statement, though not necessarily.
Therefore shows a broader scope and appears after a long descriptive 'method' leading to the proof.
QED.
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"Hence and therefore may be considered synonyms, or at least interchangeable." Don't you mean "Hence and therefore may be considered interchangeable, or at least synonyms." ? :) Oct 25, 2012 at 11:49
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1Hmm... I thought that synonyms need not be interchangeable, but interchangeables are synonyms. Oct 26, 2012 at 12:08
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