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Formal Description of sets

  1. Apr 27, 2015 #1
    1. The problem statement, all variables and given/known data

    Write formal descriptions of the following sets.

    (a) The set containing the numbers 1, 10, and 100
    (b) The set containing all integers that are greater than 5
    (c) The set containing all natural numbers that are less than 5
    (d) The set containing the string aba
    (e) The set containing the empty string
    (f) The set containing nothing at all

    2. Relevant equations

    3. The attempt at a solution

    (a) ## \{1, 10, 100 \} ##
    (b) ## \{ i\ |\ i \in \mathbb{N}\ \text{and}\ i \geq 5 \} ##
    (c) ## \{ 1, 2, 3, 4 \} ##
    (d) ## \{ aba \} ##
    (e) ## \{ \epsilon \} ##
    (f) ## \{ \} ##

    Are my answers correct?
     
  2. jcsd
  3. Apr 28, 2015 #2

    Svein

    User Avatar
    Science Advisor

    ..except that I would have written:
    (d) {"aba"}
    (e) {""}
    (f) Ø
     
  4. Apr 28, 2015 #3
    Ah! I see!

    I am fairly confident that ## \{ \}## and ## \emptyset ## mean the same thing.

    Since I am new to the representation of strings, I haven't seen the apostrophe's used for strings before, though!
     
  5. Apr 28, 2015 #4

    Mark44

    Staff: Mentor

    To add to what Svein said, the answer to (b) should be (b) ## \{ i\ |\ i \in \mathbb{N}\ \text{and}\ i > 5 \} ##
    Do you see the difference?
     
  6. Apr 28, 2015 #5
    Yes.
     
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