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If there are many service classes, and each service class has many services, is the following sentence correct?

Selecting the locally optimal service from each service class does not create a globally optimal solution.

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For what term are you struggling with the number? – bib Feb 16 '13 at 0:50
Welcome to English Language & Usage. This is off topic (writing advice). Please see the FAQ. Thanks. – MετάEd Feb 16 '13 at 1:00
@MετάEd the title is singular or plural, restricting the advice sought to whether grammatical-number is being treated correctly, rather than wider writing advice. Seems reasonably on-topic to me. – Jon Hanna Feb 16 '13 at 1:05
@JonHanna The question as presented is essentially "should I use the singular or plural in this, my sentence". As such it is still a request for writing advice. The question also needs to provide context (why am I asking or what is the text leading up to the sentence I am asking about) and the results of research done before asking here. – MετάEd Feb 16 '13 at 4:36
@MετάEd I suppose that could be "should I re-write this in a plural form", but I still read this as "am I using grammatical number correctly". Since grammatical number does relate to actual number, the info given is necessary to know if the sentence is not only grammatical correct, but has the meaning intended. – Jon Hanna Feb 16 '13 at 11:17

The sentence is grammatically correct.

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…the locally optimal service…

There is a single "locally optimal service" in each class, so this noun phrase should be singular, which it is.

…from each service class…

Unless each immediately follows a plural noun phrase (which it does not here), then what follows should be singular, which service class is.

Selecting the locally optimal service from each service class…

The gerund is used to turn the verb select into a noun, and the entire phrase above is a noun phrase for the process described, which is singular.

Selecting the locally optimal service from each service class does not create a globally optimal solution.

Three places number comes up, all of them singular, and all of them treated as singular. You're good!

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