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The speed of an object is the magnitude of the change of its position.

Speed of an object is the magnitude of the change of its position.

The second sentence seems wrong to me; I think since the "speed" in the second sentence is a property that belongs to a specific object, it is definite and should be used with the definite article. Hence, it follows that the following sentences without "the" are all incorrect.

The length of an object is how long the object is.

Length of an object is how long the object is.

The demand of a product is the number of consumers that are willing to purchase the product.

Demand of a product is the number of consumers that are willing to purchase the product.

However, I read a sentence on Wikipedia

Demand for a specific item is a function of an item's perceived necessity, price, perceived quality, convenience, available alternatives, purchasers' disposable income and tastes, and many other factors.

Is this sentence grammatically incorrect? If so, why? If not, what is the difference in meaning of the two types of sentences? What would an additional "the" do?

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  • And I think "demand" and "speed", when paired with "of an object", should be used as countables, and since each one object has one "demand" or "speed" at any given time, there should be a "the". Anyway, if "without the" is correct, I want to know the reasons so that I could use it without any doubts in the future as it is more concise. – TFR Jan 20 at 6:59
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In my opinion, none of the sentences you gave as examples are incorrect, although I generally prefer the ones you prefer. Before I would worry about the "the"s not being there, I would worry about the definitions for demand saying "number" instead of the preferable "function of" some proxy, which is still a pretty negligible offense to me. But "demand" in particular is immune to needing a "the". Also, interestingly, if you start with, say, "speed", and then put a comma, or better yet, italics and a comma (or single/double quotes), then the intent is to define the word "speed", and it is very much okay:

Speed, of an object, is...

I just think it is interesting to point out, and it breaks down some boundaries. But to restate, my impression is that all of these things are less of a problem than you think.

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  • I just read this from a book: "We often use of-phrases, such as the back of, to tell the listener which one we mean. Because something only has one back, for example, we usually use the when we talk about it, as we expect the listener to be able to work out which back we mean." The book then gives examples like "the height of" and "the length of". Is this book somehow wrong? And I think "demand" and "speed", when paired with "of an object", should be used as countables, and since each one object has one "demand" or "speed" at any given time, there should be a "the". – TFR Jan 20 at 6:51
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    Ah - I think that is a good question. Yes, in those cases, definitely us the article "the"... I think it is fair to call it incorrect not to. I say in my answer that I prefer the versions you prefer; it is just so close that I don't want to go as far as to say they are "incorrect". But I do see the argument, and it is worth knowing it is better - especially because of cases like those you listed, where it does really matter. – Justin Stafford Jan 20 at 6:58
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    I think maybe the fact that the sentences open with length or speed I am more willing to accept them, and I may be overly influenced by them sounding so much like they are speaking of the actual words, and not the qualities they refer to. – Justin Stafford Jan 20 at 7:00

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