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I am used to thinking that "within" can be used interchangeably with "inside", and Merriam-Webster seems to agree. Yet an editor of a scholarly publication marked the phrase "within the unit circle" as a usage error and noted that it should be corrected to "within the unit disk". Is he being too picky, or do the common phrases like "within reason" and "within the realm" hint that those two words are not the exact synonyms?

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  • This isn't a question of "within" vs "inside" but rather one of "circle" vs "disk". (And I frankly have never seen "unit disk" used before.)
    – Hot Licks
    Jun 24 '20 at 20:28
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    In mathematics, the unit circle is just the boundary, whereas the unit disk is the boundary plus the interior. If you're not writing an article for a mathematics journal, I don't think you need to worry about this distinction. Jun 24 '20 at 20:33
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    @PeterShor - But how could a point be within the unit disk but not within the unit circle?
    – Hot Licks
    Jun 24 '20 at 20:41
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    @PeterShor even if you are, "within the unit circle" seems to me to mean the exact same thing as "within the unit disk"; but "on the unit circle" and "on the unit disk" would be different.
    – Hellion
    Jun 24 '20 at 20:42
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    The reviewer is apparently interpreting "within" to mean "a member of the set of points defined by". I don't know if that's a common distinction to make in mathematics, but if it is it's more of a question for the Mathematics Stackexchange than for English Language Stackexchange.
    – The Photon
    Jun 24 '20 at 23:56
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A disk is a flat circular object, while a circle is an ellipse (in other words, a shape consisting of a circular line).

I suspect the editor regards the "unit disk" to be an object like a plate, rather than a simple shape, and that is the reason for the mark.

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    In mathematics, circle is the curve bounding a disk, the latter being a region of a plane. Jun 24 '20 at 20:35
  • Thank you. My math is not good.
    – RobJarvis
    Jun 24 '20 at 20:38
  • Really we shouldn't be answering this here. It is, strictly speaking, a maths question.. You need to know about intervals. Read about the subject here. basic-mathematics.com/interval-notation.html. What is the subject of your paper? What discipline? The phrase sounds mathematical and yet you claim not to know about maths. Jun 24 '20 at 21:37
  • I don't claim that, you might be confusing me with@RobJarvis. The only math knowledge required has been supplied by @PeterShor Jun 25 '20 at 10:52

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