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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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So, you don't agree with those pedants who insist not to begin a sentence with So. – Kris Oct 25 '12 at 4:01
@Kris: I agree that sentences should not begin with "and", but as far as I know beginning with "so" is okay/fine. – Tim Oct 25 '12 at 11:40
@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. – FumbleFingers Oct 25 '12 at 12:19
I always avoided using "so" in proofs when studying maths, because it could be too easily confused with "50". – Urbycoz Oct 25 '12 at 13:13
up vote 4 down vote accepted

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. – Kris Oct 25 '12 at 12:05
Btw, I find your reference interesting, any online links possibly? Reviews/ extracts even? – Kris Oct 25 '12 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.


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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." ? :) – Armen Ծիրունյան Oct 25 '12 at 11:49
@ArmenԾիրունյան I meant that interchangeables need not be synonyms. – Kris Oct 25 '12 at 11:53
Hmm... I thought that synonyms need not be interchangeable, but interchangeables are synonyms. – Armen Ծիրունյան Oct 26 '12 at 12:08
@ArmenԾիրունյան english.stackexchange.com/q/88199/14666 Interesting. – Kris Oct 26 '12 at 12:28

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