Check this definition of a subset

[setvectorgroup]

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 :)

 

[Pagan Harpoon]

I wouldn't interpret that definition as referring 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.

 

[setvectorgroup]

I wouldn't interpret that definition as referring 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.

Thank You, Pagan Harpoon.