When I want to conclude a Series of results in (math) context, I use "Hence, Therefore, So, Then ...", trying not to repeat them ; For example I don't write "A so B so C so..."; instead I write "A So B then C Hence...".
("A", "B" and "C" can be a short sentence, like "a < b", or can be as big as a paragraph).

Question 1. What is the differences among these words? Is there any priority using them in various places of context?
Question 2. can you add some other words like "Hence, Therefore, So, Then ...", (noting priority)?

Thank you.

  • 1
    Not a good idea to mix-and-match in the same statement. Try, for instance: A implies B, which in turn implies C; thus, [blah blah blah]. "so" is the most casual, with the others in rough order of formality (but depending on field of study): leads to, implies, entails, thus, hence, therefore, ergo. Use the earlier ones for simple logical statements; use the latter ones for larger, synoptic conclusions. In any case, be consistent, not random. In fiction, you can interchange these terms at will, but not in science. Check other literature in your field for examples. – Brian Hitchcock Nov 8 '15 at 9:12
  • @BrianHitchcock gives an excellent comment/answer here, I though I'd note that these terms have a strong effect on the flow of your paper. Use whichever draws the reader forward, maintaining the pace of your writing. – Will Nov 10 '15 at 18:48
  • thank you Will. I cant understand "Use whichever draws the reader forward, maintaining the pace of your writing". + I wonder if there is priority using them for a basic or long conclusion and a short one? For example if I have a paragraph and i want to drive "a < b" which one i can use? – user 1 Nov 11 '15 at 7:16

People use a variety of words in mathematical writings. The goal of using these conjunctions is to convey as precisely as possible the intended relations between the statements, and so the main criterion that people care about is whether what you write is unambiguous and flows naturally with the thought process. Usually it includes being grammatically correct, but mathematicians definitely won't ignore your work if it is clear what you're doing!

In short, it's not necessary to stick to a precise set of conjunctions, not to say attempt to fix a total ordering on them with regards to priority, unless you are writing extremely formal proofs. There are other far better ways to indicate priority, such as the hierarchy of headings, paragraphs, lines, comma-separated phrases and then phrases joined directly by conjunctions.

Of course, be careful that some terms are already defined to have very specific meaning in mathematical logic, and hence should be avoided in the first place, such as "entails". "Implies" too must be used cautiously. Consider:

If P implies Q, then R.

This is very different from say:

P, which implies Q, and hence R.

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