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If you take the number 7 out of the real number line, then

  1. Jun 17, 2013 #1
    what can be said about 7? Is it like an infinitesimal? Is it smaller or bigger? What is it? Is it just [7,7]?
     
  2. jcsd
  3. Jun 17, 2013 #2

    mathman

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    Your question is too vague. Explain what you really have in mind.
     
  4. Jun 17, 2013 #3

    Mark44

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    If you remove 7 from the number line, then you get the real numbers with a point removed. A point has zero length.
     
  5. Jun 17, 2013 #4

    HallsofIvy

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    Of the choices given, "[7, 7]", which is exactly the same as the set notation "{7}" is best. It is a single point. You would have to define exactly what you mean by "infinitesimal" in this context before anyone could answer your other questions.
     
  6. Jun 17, 2013 #5
    If I take out the number 7, then it seems as though I have something very small but perhaps larger than an infinitesimal like 5/n→∞. Because, we know that 5/n→∞ = 0, but 7 = 7, not 0.
     
  7. Jun 17, 2013 #6
    The "infinitesimal" that I was thinking of is something like 3/n→∞.
     
  8. Jun 17, 2013 #7

    Office_Shredder

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    What you've written doesn't make any sense. Did you mean something like
    [tex] \lim_{n\to \infty} \frac{3}{n} = 0 [/tex]?

    It's not clear to me why you think this is related to the number 7. The length of the interval [7,7] is completely unrelated to the number 7 itself
     
  9. Jun 17, 2013 #8
    Yes, I just don't know how to use the proper notation on this forum.

    Doesn't [7,7] and 7 have similar properties?
     
  10. Jun 17, 2013 #9

    Office_Shredder

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    Does [tex] \mathbb{R} [/tex] and [tex] \{ \mathbb{R} \} [/tex] have similar properties? The first being the set of real numbers, and the second being a set which contains a single element, namely the set of real numbers. The answer is no, not in general. Another good example is ∅, the empty set, and {∅}, the set containing only the empty set (in particular it is not empty!)

    Any claims that [7,7] (which is the set containing only the number 7, i.e. {7} as has been mentioned above) and 7 the number share similar properties should be clarified in detail: what properties might these share?
     
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