Expresssing the number of objects

Is the following sentence grammatically correct?

G is generated by 2k+t number of 7-cycles.

Edit: I found the following expressions

then the product set A X B has the arithmetic n X m number of elements.

If A[21] is the array to be checked and the maximum value that it stores is M, then take another array B[M] with M number of elements.

which convinced me that my sentence is correct.

• Shouldn't that be 'numbers'? Commented Apr 13, 2016 at 6:21
• I do not know!! Commented Apr 13, 2016 at 6:35
• Without context, neither do we. Commented Apr 13, 2016 at 6:38

To a mathematician, these look horrible. Much better is simply

G is generated by 2k+t 7-cycles.

and

then the product set A x B has n x m elements.

I understand that the first writer (was it you?) was reluctant to leave t and 7 so close together, but my version is clear enough. As for your second example, it looks more like a train crash than a sentence -- perhaps it was a cut-and-paste error.

I'd prefer to put a determiner before 2k+t number.

• like this: G is generated by some 2k+t number of 7-cycles? Commented Apr 13, 2016 at 6:21
• I think 2k+t number is a formula here. Maybe the sentence should be something like this: "G is generated by a 2k+t number of 7-cycles." Commented Apr 13, 2016 at 6:26
• If you have any other clarifications regarding this, kindly don't hesitate to ask. If you think I was able to answer your question, please don't forget to accept the answer. Thanks Commented Apr 13, 2016 at 6:39
• I'd prefer a verb. G is generated by running 2k+t number of 7-cycles? Commented Apr 13, 2016 at 15:15
• Well, there are lots of ways to construct proper sentences. Commented Apr 14, 2016 at 0:46

Your example uses the form G is generated by X number of Ys, with complicated forms of X and Y.

Let's look at another (equivalent) example first for simplicity: juice is generated by five number of machines. Although there are instances where this form is used, e.g. "My land runs 5,000 head of cattle." (- Wikipedia), the form is more often written simply as juice is generated by five machines, dropping the phrase "number of".

Returning to your example, you would simply have G is generated by X Ys, or with your original terms, G is generated by (2k+t) 7-cycles. I have inserted brackets to reduce ambiguity, but the presence of two mathematical expressions so close to each other is non-ideal.

Number is awkward in this context since it doesn't identify any part of the unit (7-cycle). If these 7-cycles are periodic, try G is generated by 2k+t periods of 7-cycles. Otherwise, choose some identifying aspect of the 7-cycles to use instead of periods.

Finally, a note about plurality. "head of cattle" (with the singular form head) is a specialist term in this context. In the form X 'count(s)' of Ys, the word used in place of count(s) should normally be singular if X=1 and plural otherwise. The word used in place of Ys should normally be plural. If we used the simpler form X Ys, then we would use a singular form for Ys if X=1, and a plural form otherwise.

Returning to the juice example, the following are all grammatically correct:

• Juice is generated by one machine.
• Juice is generated by five machines.
• Juice is generated by one group of machines.
• Juice is generated by five groups of machines.

In your case, if you retain the algebraic expression 2k+t, then periods should be always be plural.

• @PhilSweet Thanks for taking the time to point out the issue about grammatical number. I now see what you were getting at and have addressed it in my edited answer. Let me know if I've read your point correctly. Commented Apr 13, 2016 at 16:55
• @ lawrence I've cleaned out the old comments. Commented Apr 13, 2016 at 17:09
• Consider "juice is now being produced by half the number of machines" vs "juice is now being produced by half the machines". "Number" here is a placeholder for a longer phrase such as "number that we used to use". And I suspect "number" in the OP's example replaces "number of cycles". When I mentally unpack the OP's sentence, I end up with "G is generated by 2k+t number of cycles of 7-cycles (or number of periods of 7-cycles). Which is a long way of getting around to saying I think the singular number is correct here. I would write it as "G is generated by running 2k+t interations of 7-cycles. Commented Apr 13, 2016 at 20:38
• On half: the shorter X Ys pattern holds for your first 2 examples: X="half the number of" Ys="machines"; and X="half" Ys="the machines". On number of: the phrasing still sounds awkward when there is an actual number before the phrase (5 number of cycles/periods); the plural 5 numbers of periods sounds marginally better but still awkward. The number 2k+t already names how many, so 2k+t number of periods of sounds like the doubled phrase number number of periods of. On iterations replacing periods - yes, that can work. Commented Apr 13, 2016 at 23:36