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Intermediate analysis homework

  1. Sep 4, 2011 #1
    For (c), it looks like this set goes off to negative and positive infinity.

    http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20110904_125145.jpg [Broken]

    For (e), I think this is right. Since r is in the rationals, r gets arbitrarily close to the square root of 5, so there are no particular numbers that are the min, max of the set. Also, since r is in the rationals, there is no particular number that is the sup or inf.

    http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20110904_125117.jpg [Broken]

    For (f) and (g), the "limit" of the intersection and union appears to be the open interval (0,1). If that's the case, the answers should be the same. Since it is an open interval, 0 and 1 are not elements of the set, so there is no particular number that is the min, max. But, I could say 0 and 1 are the inf and sup, respectively. I'm not too sure about this.

    http://i111.photobucket.com/albums/n149/camarolt4z28/IMG_20110904_125132.jpg [Broken]
    Last edited by a moderator: May 5, 2017
  2. jcsd
  3. Sep 4, 2011 #2
    C looks right, I'm pretty sure if you don't have a sup or inf, then you can't have a min or max.

    I can't help you out with F and G. But, look at E again, you sure about that? Start by writing out some actual numbers within that set.
  4. Sep 4, 2011 #3
    Yes. I'm sure on (e). The smallest and largest number you could have is -sqrt5 and sqrt 5. However, since r is in the rationals, that's not a valid number. You can always find a rational number that's arbitrarily close to sqrt 5. So, there is no min and max. But, I guess I could say the inf and sup are -sqrt 5 and sqrt 5, respectively.
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