Using Comma in if...then Conditional Sentences

Question

Many English grammar books state that in an "if ... then" conditional sentence, the word then should be preceded by a comma. However, in mathematical writing I often see that this rule is ignored.

Here is a sentence taken from Higham's Handbook of Writing for Mathematical Sciences:

If $\alpha>-1$ then the integral does not exist.

Since the book is intended for writing mathematics correctly and this structure has appeared in many places inside it, lack of a comma in the above sentence cannot be a simple typo. Does anyone know the reason for this?

Added in Edit: As a separate, but related question, would it be possible that the omission of comma is due to the conditional sentence ending with a mathematical formula?

Answer 1

If the premise of a conditional statement is so tediously, extraordinarily, and inordinately long that it is easy to lose track of its train of thought, especially when the premise contains many, many, many, many commas and subordinate clauses, then using a comma before the concluding clause may well be beneficial.

If the premise is short then the lack of comma doesn't really hinder understanding.

If it were up to me, I would always use a comma.

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By the way, the 16th edition of The Chicago Manual of Style suggests that “[a] dependent clause that precedes a main clause should be followed by a comma,” and uses the following example (see 6.30, p. 317):

If you accept our conditions, we shall agree to the proposal.

I believe this rule applies also when a “then” is added to the beginning of the concluding clause.

Answer 2

My answers to the question' Why do mathematical if-then statements often miss out the comma after the if clause?' would be:

1) Mathematicians try to keep things simple & clear, and in scruffy handwriting a comma might be mistaken for something else by the reader;

2) The comma rule is not so strictly adhered to among other English users anyway;

3) Typical if-then statements in ordinary life have more contingency and uncertainty to both sides of the if-then statement than they do in maths. For example, in a legal if-then sentence both sides can be debatable ...only true with certain clarifications. In "If the client's property is damaged by an act of terrorism, then...", for example, there can easily be debate in court as to whether a given event qualified as matching the content of the if clause. In contrast, maths readers are typically willing to accept the if clause as "transparent", not needing debate (if it is unclear, they often reject the whole sentence or document as unclear), so that "If x > 2" requires no special consideration, no discussion as to whether x is or is not greater than 2. The maths reader simply accepts this clause and moves straight on, hence "If x > 2 then y ...whatever" does not look strange without a comma;

4) A commonly stated rule of thumb in English is that commas give the reader a chance to take a breath. For reasons similar to those in (3), maths readers are less likely to wish to take a breath or a pause. The if-then statement has the feel of a complete unit for mathematicians, and they want to "take it whole".

Strangely, most children in most English-speaking countries attend school without ever being given grammar lessons in their own language. To clarify reason (2) above it would be interesting to hear from mathematicians who write their first drafts (or all drafts!) in a language where grammar of the native language is a compulsory subject at school: German or French or Russian speakers on here? Do you automatically carry over all the punctuation rules of your first language into the mathematical sentences you write?