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Fact: Each object has a speed parameter

Which of the following grammatical and sounds better?

We use the symbol c[t1] henceforth, where c is a speed function and t1 is a speed parameter for an object obj1.

We use the symbol c[t1] henceforth, where c is a speed function and t1 is a speed parameter for some objects obj1.

We use the symbol c[t1] henceforth, where c is a speed function and t1 is a speed parameter for any object obj1.

We use the symbol c[t1] henceforth, where c is a speed function and t1 is a speed parameter. (just omit it)

what I want to say is that obj1 is just any object, not a particular one.

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I like this the best:

We use the symbol c[t1] henceforth, where c is a speed function and t1 is a speed parameter for any object obj1.

However I think it sounds better as this:

We use the symbol c[t1] henceforth, where c is a speed function and t1 is a speed parameter for any given object.

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  • "for any given object", this sounds very cool :)
    – william007
    Commented Jul 3, 2013 at 11:17
  • lonehorse, so there is no need to indicate 'obj1' because from the context one argues that 't1' is related with?
    – user114
    Commented Jul 3, 2013 at 17:40
  • It's hard to tell, because we don't have the context for william007's sentence. In his original statement, he said "what I want to say is that obj1 is just any object, not a particular one," so I just went off of that.
    – lonehorseend
    Commented Jul 3, 2013 at 18:11
  • I think I would use "a given object" here, assuming that one instance of t1 is a parameter for one instance of an object. It isn't "any" object in this case, it's the object to which the parameter t1 is related.
    – BobRodes
    Commented Jul 4, 2013 at 2:39
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The index 1 appears to imply that there may be multiple objects, each with its own speed parameter:

obj1 has speed parameter t1
obj2 has speed parameter t2, and so forth.

If this is the case, when you say that "obj1 is just any object, not a particular one" you do not mean that t1 may be associated with any object; you mean, rather, that any object may be represented by obj1, but whatever specific object is represented has a specific associated t1.

But the very representation of an object in the abstract form obj1 will ordinarily lead your readers to assume that obj1 is a variable, capable of representing "any" object. "Any", in that limited application, will be understood.

Consequently, I would suggest:

t1 is the speed parameter associated with an object obj1.

And you might consider replacing 1 with n, the conventional representation of an integer variable:

We use the symbol c[tn] henceforth, where c is a speed function and tn is the speed parameter associated with an object objn.

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