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Check this definition of a subset

  1. Mar 10, 2013 #1
    1. The problem statement, all variables and given/known data

    "We say a set T is a subset of a set S if every element of T also belongs to S( i.e T consists of some of the elements of S). We write T ⊆ S if T is a subset of S and T ⊄ S if not. For example, if S = {1, {2}, cat}, then {cat} ⊆ S, {{2}} ⊆ S, 2 ⊄ S.

    As another example, the subsets of {1,2} are {1,2}, {1}, {2}, Ø.

    By convention, Ø is a subset of every set."
    3. The attempt at a solution

    Is the definition above describing a proper subset without mentioning it by name? Because the bold part of the text above seems to be alluding to T < S. But the italicized part is saying that a set is its own subset.

    The reason I ask this because I have a problem that I dont know how to approach because the above quote is confusing me a bit.

    Thanks.

    edit: I meant to start my title with "Please', but somehow forgot to put it there. Sorry for that infraction :)
     
    Last edited: Mar 10, 2013
  2. jcsd
  3. Mar 10, 2013 #2
    I wouldn't interpret that definition as refering to a proper subset. The part in italics seems to make it pretty clear that it considers every set to be a subset of itself.

    I don't think the part in bold contradicts that. It says that a subset of S must consist of some of the elements of S, but it doesn't say the subset can't contain all the elements of S.
     
  4. Mar 11, 2013 #3
    Thank You, Pagan Harpoon.
     
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