Right Punctuation in Equivalent Conditions

Question

The sentence "The following are equivalent:" is frequently used in mathematics, and most of the time it is followed by a list of statements.

It was never clear to me how one should seperate these statements, so I did it by intuition. But today a colleague told me that in the English language it is done by writing semicolons between these statements.

I checked this in several papers of English native speakers and found quite different notations but no semicolons at all.

Now I am a bit confused and would appreciate any help or reference. Thank you in advance!

Answer 1

There is no universal 'correct' definition. The key point is that it is easy to understand what you mean. If there are more than two statements I would prefer a list of bullet points, like so.

The following are equivalent:

• List item 1
• List item 2
• List item 3

Continuation of text.

Answer 2

Typically, list items should be separated by either a comma or a semicolon. A comma should be used for separating simple clauses, while semicolons should be used for more complicated phrases. It may also be appropriate to use periods at the end of each list item, if these list items are themselves complete sentences. That being said, this is a matter of style and taste, and there is no universal "right" answer. Your best bet is to consult the style guide of whatever journal you are aiming for.

For example, the American Math Society style guide addresses the punctuation of lists in Section 6. The relevant guidelines are

6.3. Punctuation and capitalization

• Every entry must be punctuated (see section 6.5).
• Only those entries that are complete sentences are capitalized; phrases are lowercase (see section 6.5.4).

and 6.5. List examples, which I will not reproduce here. You will note in the examples that there are lists in which each item ends with a period, there are several examples with semicolons, and one example with commas (the last example of 6.5.5 on page 43).

Answer 3

Two versions I know and use, also compatible with English grammar.

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The following statements are equivalent.

1. Statement $A$.
2. Statement $B$.

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The following statements are equivalent:

$a)$ statement $A$;
$b)$ statement $B$.

One may also use Roman numerals for listing: $i, ii, iii, iv, v$ etc, though, I've rarely seen this option.