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italicizing defined terms, defining V(n), questionable word usage, and providing examples
Perhaps I should file each of these as separate corrections, but that would be somewhat tedious, and this is more concise.
1. With the exception of "unit sphere", all terms defined in this entry are italicized. Could you please italicize the first occurrence of "unit sphere" in this entry?
2. The function that you define as V(n) is actually dependent on r also. Perhaps it would be a good idea to emphasize this dependence by letting V take two arguments: V(n,r).
Unfortunately, if you do this, you may have to amend your statement regarding the volume going to zero. Perhaps something like: "For fixed r, V(n,r) tends to zero as n approaches infinity."
3. After giving the formula for V(n), you state that:
V(n) has a maximum at about n=5 for the unit sphere.
I would recommend killing the word "about". Unless dimension does not have to be a natural number (a phenomenon that I have not encountered yet), V(n) has a maximum at precisely n=5 for the unit sphere. (Actually, if you change V as suggested earlier, you could instead say that V(n,1) has a maximum precisely at n=5.)
4. I would recommend providing examples of how to calculate V(n) (or V(n,r)). This would be most useful for backing up the claim that V(n,1) achieves its maximum value at n=5.
If you would prefer that I file corrections separately in the future, please let me know. Thanks.
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