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## Main Question or Discussion Point

My book defines a proper subset: "a Set A is a proper subset of a set B if A [tex]\subseteq[/tex] B but A [tex]\neq[/tex] B. If A is a proper subset of B we write A[tex]\subset[/tex]B."

For example, S={4,5,7} and T={3,4,5,6,7}, then S [tex]\subset[/tex] T.

So, from my understanding, every element in S is contained in T however there is at least one other element in T not contained in S.

So what would an example of A[tex]\subseteq[/tex]B be?

My text says the [tex]N[/tex][tex]\subseteq[/tex][tex]Z[/tex] (Natural numbers and integers, respectively).

But every element of [tex]N[/tex] is contained in [tex]Z[/tex] and they are not equal, so wouldn't we write [tex]N[/tex][tex]\subset[/tex][tex]Z[/tex] ?

What would be an example of three sets A,B,C such that A[tex]\subseteq[/tex] B and B [tex]\subset[/tex] C ? (the notation is coming out funny looking for some reason... "A is a subset of B and B is a proper subset of C", is what I'm trying to say.

Would this be correct...

A={1,2,3}, B={1,2,3}, C={1,2,3,4} ?

Or would this be correct...

A={1,2,3}, B={{1,2,3}}, C={{1,2,3},4}

For example, S={4,5,7} and T={3,4,5,6,7}, then S [tex]\subset[/tex] T.

So, from my understanding, every element in S is contained in T however there is at least one other element in T not contained in S.

So what would an example of A[tex]\subseteq[/tex]B be?

My text says the [tex]N[/tex][tex]\subseteq[/tex][tex]Z[/tex] (Natural numbers and integers, respectively).

But every element of [tex]N[/tex] is contained in [tex]Z[/tex] and they are not equal, so wouldn't we write [tex]N[/tex][tex]\subset[/tex][tex]Z[/tex] ?

What would be an example of three sets A,B,C such that A[tex]\subseteq[/tex] B and B [tex]\subset[/tex] C ? (the notation is coming out funny looking for some reason... "A is a subset of B and B is a proper subset of C", is what I'm trying to say.

Would this be correct...

A={1,2,3}, B={1,2,3}, C={1,2,3,4} ?

Or would this be correct...

A={1,2,3}, B={{1,2,3}}, C={{1,2,3},4}