1

Consider the sentence

The net simulates programs with at least 𝑓(π‘₯) copies of each π‘₯ βŠ† 𝑆 with πœ‘(π‘₯) (,) and exactly 𝑓(π‘₯) copies of each π‘₯ βŠ† 𝑆 with πœ“(π‘₯).

The parens around the comma mean that it's unclear whether the comma belongs there. The terms πœ‘(π‘₯) and πœ“(π‘₯) are Boolean formulas in which π‘₯ occurs and which can be shown to be logical negations of one another for all π‘₯ βŠ† 𝑆.

Is the comma before β€œand”

  1. forbidden,

  2. necessary,

  3. optional with a change in the meaning, or

  4. optional without a change in the meaning?

Why?

1
  • Frankly this is not an appropriate question for "English learners". You are apparently a native speaker (or good enough) and you are asking about fairly high-level mathematical notation (at least university level?). Usually the kind of stuff I see on LaTeX talk! ha.
    – equin0x80
    Commented Oct 14, 2022 at 11:18

1 Answer 1

1

The net simulates programs with at least 𝑓(π‘₯) copies of each π‘₯ βŠ† 𝑆 with πœ‘(π‘₯) (,) and exactly 𝑓(π‘₯) copies of each π‘₯ βŠ† 𝑆 with πœ“(π‘₯).

This is a simple sentence. The two noun phrases at least 𝑓(π‘₯) copies of each π‘₯ βŠ† 𝑆 with πœ‘(π‘₯) and exactly 𝑓(π‘₯) copies of each π‘₯ βŠ† 𝑆 with πœ“(π‘₯) are parallel and are objects of the first preposition, with.

We usually do not use commas when joining the two items or phrases of a compound object. Exceptions could apply if the phrases are long or complicated, as in this case; the two noun phrases here even have their withs.

A comma would give clarity. This is optional without affecting the meaning of the sentence.

Please see reference for examples of exceptions, including the following one.

The exception to the simple sentence rule is if omitting the comma will make the sentence confusing.

Grapes are as good for you as bananas, and apples even more so.

1
  • Thanks! I interpret β€œGrapes are as good for you as bananas and apples even more so.” as β€œGrapes are as good for you as bananas. In terms of being good for you, apples are closer to bananas when compared with how close are grapes to bananas.” What would constitute a confusing misreading of β€œGrapes are as good for you as bananas and apples even more so.” ?
    – user142975
    Commented Dec 21, 2021 at 9:39

You must log in to answer this question.