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number all of whose digits follow the indicated pattern, ie., 0.999...;...999... (borrowing
Lightstone's notation). This number is 1. As it is open to interpretation, it is not a very instructive picture. Also it uses the notion of a non-standard microscope which would only make sense to people having read Keisler's book.
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I did not think you were unaware of uniqueness problems. In a non-standard setting there is not a agreed upon convention for which number 0.999... means. You seem to to take the position that it represents some number whose standard part has infinitely many nines. My interpretation would be the
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It was not clear to me that you intended an unbounded hyperinteger, and perhaps many unfamiliar with NSA might have the same confusion at first glance. I don't doubt that students relate to the idea with enthusiasm, I just felt this image was unclear. I have no problem with discussing a
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The image here doesn't make sense, and is poorly produced. The number display's the decimal 0.9999.... (with infinitely many 9's) as being different then 1. Which is simply false. For this reason I am removing the picture from the article until it can be discussed further.
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and no further. In my experience, students relate to these ideas with great enthusiasm. The infinite-magnification microscope is an idealized concept that has proven classroom utility.
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I suppose it did not occur to you that I may be familiar with the non-unicity of decimal representation of the reals :) Could you please take a look at the current discussion at
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