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"The roots could be any arbitrary distance apart."
"The roots could be an arbitrary distance apart."

Using "any" is more redundant as I could take out "arbitrary" and it would still make sense (although it wouldn't quite convey the meaning I want), but it flows better than "an". Hence, would it be better to use "any" for the sake of flow or "an" for the sake of non-redundancy?

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Any and an are two completely different words, so it's hard, or just odd, to compare their usage. Explain what you mean to convey and that might help. –  Alenanno May 26 '11 at 17:09
    
@Alenanno: Well, I am a mathematician as well, so I am referring to the roots of a polynomial (those things you learned about in middle/high school), or where it equals zero. I'm writing about a method that uses a particular characteristic of polynomials to find the zeros...which could be anywhere. I want to emphasize the fact that there are no restrictions. –  El'endia Starman May 26 '11 at 17:22
    
More context would help. Arbitrary implies there's an element of choice, but the particular choice made makes no difference. If these were roots of a tree, for example, arbitrary would be odd, because the tree doesn't meaningfully choose where to put its roots. If it's some mathematical operation involving square roots that works with any arbitrarily chosen values, you can use long words without seeming gratuitously verbose. –  FumbleFingers May 26 '11 at 17:23
    
@El'endia Starman: posts crossed, sorry. –  FumbleFingers May 26 '11 at 17:25
    
@FumbleFingers: No problem. I figured you would see mine after yours and get the answer to your (implied) question. –  El'endia Starman May 26 '11 at 17:27
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4 Answers 4

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There is one context I can think of where the two sentences will differ significantly: if the action (planting bushes?) is repeated.

An arbitrary distance implies that you chose one arbitrary distance for spacing all of them.

while

Any arbitrary distance tends to allow for different distances being selected for each spacing.

"Implies" and "tends to" are my weasel words for admitting that these are not hard-and-fast differences. Either interpretation is possible, but I would tend to use the an/any distinction myself to indicate the (lack of) variation.

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The context is not the same, but you make a very good point. In fact, in my true context, this lends support for "any". –  El'endia Starman May 26 '11 at 18:23
    
+1 for excellent fine distinction, even if it's not OP's actual concern here! –  FumbleFingers May 26 '11 at 19:08
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I prefer #2, in my opinion it flows better. The stress falls on roots and arbitrary which together carry most of the meaning of your sentence.

I noted also that more in 'more redundant' is itself redundant.

Just thinking about redundancy in speech and writing, it's something I try hard to avoid when writing technical documents. I prefer to find the most accurate and concise expressions I can. In everyday writing, however, it is often tempting to use redundancy for rhetorical purposes or preserve rhythm.

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Good catch about the "more redundant" part... -_- Anyway, yeah, I do the same thing when writing about math for laypeople and I always try to find a balance between flow and correctness. –  El'endia Starman May 26 '11 at 17:29
    
+1 for pointing out the more reduncancy. Which isn't so bad as the actual tautology of any arbitrary. –  FumbleFingers May 26 '11 at 17:58
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I'm interested in the context of this sentence. It seems that "arbitrary" is entirely redundant, or at least seems incompatible with "could". I am guessing that your intent is either:

"The roots could be any distance apart."

"The roots are an arbitrary distance apart."

When I read "the roots could be an arbitrary distance apart", I get the implication, "the roots are a certain distance apart, and the distance might be determined by a logical rule, or the distance might be determined entirely capriciously."

"Could" here seems to refer the fact that you are not sure if the distance is arbitrary, rather than the fact that you are not sure what the distance is.

But maybe that is your intent, or maybe I am off base.

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I'm with z7sg in thinking the second form ("an") flows better. That's not the whole story, though; the "any" version does add considerable emphasis to the arbitrariness of choice of roots, so may be more appropriate if that is the point you want to bring out.

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