"Assume that A = B" subjunctive?

Question

Over on Math.SE, a question exists regarding the usage of the word "that" in the following sentences:

1. Assume that A = B.
2. Assume A = B.

A well-known author suggests that users elect Option 1 in mathematical writing.

A discussion arose whether or not Option 1 is perfectly acceptable usage of the subjunctive, with a caveat: that the glyph "=" be read "equal" and not "equals."

The author of the book in question also further suggested that the word "that" be used only if it helps parse a sentence, "Assume that A is a group" vs. "Assume A is a group." This point was less contended, but in the subjunctive discussion, contrary concerns also arose whether the usage "Assume A be a group" is correct archaically, is correct presently, or has never been correct at all.

First question: given that "Assume..." is functionally equivalent to necessity in mathematical writing, is the sentence "Assume that A equal B" a proper use of the subjunctive?

Second question: Is, or has ever been, the usage "Assume that A be a group" been proper conjugation of "is" in a properly-used subjunctive?

Third question: Is there anything structurally unsavory about the use of the conjunction "that" in the form "Assume that A equals B" (note the s)?

Answer 1

1. Patterning of the subjunctive is becoming very spotty in English, but is generally restricted to subordinate clauses licensed by verbs of compulsion or persuasion. e.g., The court orders/requests/requires/prays that Thomas present himself for sentencing... [pray used in its legal sense]. In modern American English (I don't know about older English) the preceding sentence doesn't work with psych verbs like hope/wish/pray [pray used in its common sense] or cognition verbs like think/assume/believe/suppose. Note also that the modal use of were (e.g., Assume that Thomas were guilty...) is usually called irrealis, not subjunctive.
2. That is correct, but only because let licenses a complement clause with its verb in the base form. It doesn't have to do with the subjunctive. (e.g., The judge let Thomas delay the hearing... is clearly not showing subjunctive mood)
3. Nothing structurally unsavory, and I agree that the best guideline on omitting or using that is to improve parseability.

Answer 2

Your “well-known author” doesn’t seem to know English very well.

The verb assume always takes the indicative in contemporary English. The correct formulation is:

I assume that he is coming.

And therefore, of

Assume that A is equal to B.

or likewise

Assume that A equals B.

You can find people who might say

Suppose it were otherwise; what would you do?

Imagine that it were different; what would you do?

But there aren’t many of those.

As for your second question,

Let A be a group.

Is perfectly grammatical.

Finally, on your last question, there is nothing whatsoever wrong with having a that there, any more than there is anything wrong with not having it there.

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Edit

I suppose it might be possible that your writer is using assume as a substitute for let, making it a sort of auxiliary. It would therefore take a bare infinitive under that reading.

However, the OED presents no documented evidence of that sort of thing. The only thing of apparent relevance which the OED gives is this:

10. trans. To take for granted as the basis of argument or action; to suppose: a. that a thing is, a thing to be.

• 1841 Myers Cath. Th. iii. §25. 91 — To assume that we have the most accurate possible translation.
• 1868 Peard Water-farm. x. 103 — The entire length of our farm is assumed to be about thirty-two miles.

There you have documentation that it takes both that and a simple indicative is form: one assumes that a thing is such and such.

Answer 3

All right, the English subjunctive mood is tricky mostly because, in modern English, it's considered in many areas to be moribund or outmoded. In most situations, the indicative and subjunctive can live side by side and have, in fact, done so since Middle English times. I went to school for English and many of my theses have been written on this topic. I shall break down the subjunctive, which can have a very formal, sometimes archaic feel to it, but is still quite beautiful, to say the least. Here are some examples in the subjunctive mood (some examples may have a modal that replaces the subjunctive forms):

1. Assuming that he be correct, can we still get to the show in time?

2. "And ne'er throughout the year to church thou go'st/Except it be to pray against thy foes" (Shakespeare).

3. I pray that God give them the serenity that they may forgive this man.

4. O that I were the President of the United States. What policies I would invoke were I holding that office.

5. I can only hope that he find true love one day. It's my only hope and wish that he be as lucky as I have been in my lifetime with my wife.

6. Should he violate the terms of his parole, he shall be returned to prison forthwith.

7. Whether the committee sanction him or not, he will still remain in his tenured position on the board.

8. It is important that the students do their own work.

9. I demanded that they not say another word.

10. Though he face many perils, he will ultimately succeed. (Also, though he may face many perils...).

11. It's better if he go with you.

12. If you had gone to school, you would have had to take a test.

13. I wish I were an Oscar Meyer wiener.

14. If only he knew the answer, he wouldn't be in this predicament.

15. It is the judgment of this court that you be sentenced to probation.

16. He will be permitted to attend the ceremony provided he dress accordingly.

17. We shall do it on the condition that we be paid $5,000.

18. In the event that he died right now, his estate would devise to his next of kin.

19. As long as he have answered all of the questions, the chances of his failing are slim.

20. They will plant trees along the street in memory of the victims so that no one ever forget them.

21. If he go to the store, he will buy some eggs.

22. If I were to go with you, I would never forgive myself.

23. He fled the country lest he be captured and imprisoned.

The above examples are all correct under the rules of English grammar; however, many of them would be considered archaic if they were used today. Despite their being overly formal or archaic, they limn the usage of the subjunctive in English in a diachronic analysis more so than just capturing its modern usage. None of the 23 examples above could be deemed ungrammatical, but many people might categorize them as stilted nonetheless. These examples were not shown to be stilted; they were shown so that readers could see the entire usage of the subjunctive.

The subjunctive can be used after many other coordinating conjunctions like "until", "unless", "although", and "before". It can also be used after subordinating "that" clauses when those clauses are linked by words of necessity, possibility, contingency, commands, requests, aspirations, supplications, doubts, fears, and other operative words that evoke latent emotions that do not necessarily indicate that an event happens, will happen, or has happened. Those words that would indicate such actual events would fall into the indicative mood, which is the common mood of language: "He is the one. I went to the store yesterday. They will find the time to do it."

That is the English subjunctive mood in a nutshell. One example I did not discuss, "Let there be light", is called the hortatory subjunctive so those above who proclaimed that "let" doesn't open up a subjunctive are wrong.