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setvectorgroup
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Homework Statement
"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."
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 don't 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 :)
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