"Theorems 1 and 2 imply" vs. "Theorem 1 and Theorem 2 imply"

Question

To convey that $$\text{Theorem 1} \wedge \text{Theorem 2} \implies A$$ which style is better?

Theorems 1 and 2 imply $A$.

Theorem 1 and Theorem 2 imply $A$.

Which style manuals prefer which form?

(This question concerns the repetition of the word theorem, not the capitalization.)

Chicago Manual of Style has a math chapter, AMS style guide... no style guide can cover every situation, but if there is a style guide that speaks to this issue, I would like to know, and it is helpful to have such questions on SE because the style guides themselves are often paywalled. — Max, Jan 01 '22 at 07:08
Looks better to me too, but when I am asked to offer stylistic comments on someone's paper, I try to justify them with reference to a style manual, hence the question. — Max, Jan 01 '22 at 07:14
I can't speak to what style manuals, but I prefer "Theorems 1 and 2". Consider the extrapolation where more theorems are involved. Would you really want to write "Theorem 1, Theorem 2, Theorem 3, ..., and Theorem $n$ imply ..." vs "Theorems 1, 2, 3, ..., $n$ imply ..."? ... In any case, if the Chicago Manual has guidance regarding "Presidents Smith and Jones" vs "President Smith and President Jones", then perhaps that would apply here. The Writing StackExchange may have insights. — Blue, Jan 01 '22 at 07:19
I agree with your preference. For the purposes of this question, I'm looking for something more than a well-reasoned opinion--ideally a reference to a style manual, or failing that, quotations from well-copyedited, published references. — Max, Jan 01 '22 at 07:24
I would look for articles by a native speaker... e.g. a British or American author born in UK or USA, respectively. — Medo, Jan 01 '22 at 07:39

score 4 · Answer 1 · answered Jan 01 '22 at 08:26

4

Besides style, I think there's an issue of ambiguous interpretation:
"Theorems 1 and 2 imply..." suggests to me that $\mbox{Thm}1\ \&\ \mbox{Thm}2\Rightarrow\mbox{Thm}3$.
But "Theorem 1 and Theorem 2 imply..." might more easily be interpreted to mean
$\mbox{Thm}1\Rightarrow\mbox{Thm}3\ \ \&\ \ \mbox{Thm}2\Rightarrow\mbox{Thm}3$

answered Jan 01 '22 at 08:26

eigengrau

286

1

The same ambiguity is present in either construction. A less ambiguous way to convey the latter meaning is "Theorem 1 or 2 implies ... " or "Theorems 1 and 2 alike imply ..." – Max Jan 03 '22 at 00:22
@Max Sure -- I was trying to suggest that you might want to partition your question into two sub-questions: which style is best when you mean one thing, versus which style is best when you mean the other. – eigengrau Jan 04 '22 at 07:57

ryang · Answer 2 · 2023-07-03T08:09:49.560

Theorems $1$ and $2$ imply $A.$

Theorem $1$ and Theorem $2$ imply $A.$

The first phrasing is a tad more idiomatic than the second one, but nonetheless, they are in practice equivalent: each can be construed as either statement $(\text A1)$ or statement $(\text A2)$ below (admittedly, the $(\text A1)$ reading is a little more immediate)!

Suggestions:

$(\text{Theorem 1} \wedge \text{Theorem 2}) \implies A\tag{A1}$

Theorems $1$ and $2$ collectively/together/jointly/conjunctively implies $A.$
$(\text{Theorem 1} \implies A) \land (\text{Theorem 2} \implies A) \tag{A2}$

Theorems $1$ and $2$ each implies $A.$

Notice that adding the word ‘both’ to the two phrasings at the top doesn't aid disambiguation.

Theorem $1$ or $2$ implies $A.$

Theorem $1$ or Theorem $2$ implies $A.$

You didn't ask, but these ‘or’ phrasings have the same issue as above.

Suggestions:

$(\text{Theorem 1} \lor \text{Theorem 2}) \implies A\tag{O1}$

If Theorem $1$ or $2$ is true, then $A$ is true.

Theorems $1$ and $2$ each implies $A.\quad$ (I.e., statement $(\text A2)$.)
$(\text{Theorem 1} \implies A) \lor (\text{Theorem 2} \implies A) \tag{O2}$

Theorem $1$ implies $A$ or Theorem $2$ implies $A.$

Theorems $1$ and $2$ jointly implies $A.\quad$ (I.e., statement $(\text A1)$; proof)

"Theorems 1 and 2 imply" vs. "Theorem 1 and Theorem 2 imply"

2 Answers2