The discussion revolves around proving the inclusion of power sets, specifically addressing the claim that if set A is a subset of set B (A ⊆ B), then the power set of A (P(A)) is a subset of the power set of B (P(B)). The scope includes theoretical aspects of set theory and formal proof techniques.
Participants generally agree on the approach of starting with definitions and the nature of elements in power sets. However, there is no consensus on the specific method to proceed with the proof, as some participants express different inclinations on how to initiate the argument.
Limitations include potential misunderstandings of the definitions of subsets and power sets, as well as the need for a formal structure in the proof that remains unresolved in the discussion.
This discussion may be useful for students studying set theory, particularly those looking for insights into formal proofs involving power sets and subset relations.
im2fastfouru said:i'm more inclined to start with x [tex]\in[/tex] P(a), can i start the proof this way?
Why do you say "more inclined"? That was exactly what was suggested.im2fastfouru said:i'm more inclined to start with x [tex]\in[/tex] P(a), can i start the proof this way?
im2fastfouru said:i'm more inclined to start with x [tex]\in[/tex] P(a), can i start the proof this way?
what is x? In particular, what set are all of x's elements in?
im2fastfouru said:x is just an arbitrary element. And if A [tex]\subseteq[/tex] B then prove P(A) [tex]\subseteq[/tex] P(B). This need to be proved formally as well for my assignment!