Recent content by dainty77

Actually not cases, but by a direct proof so: let n^4=(n^2)^2 Let n be an odd number Then n=2k+1 for some integer k then n^2= (2k+1)^2 =4k^2 + 4k +1 =2(2k^2+2k) + 1 I don't think this is proving anything. I will try something else

Homework Statement If n is a natural number, then n^4 ends in either zero, one, five, or six. Homework Equations The Attempt at a Solution Should I attempt this by cases?

I see where you are gettiing at! Let me work on it some more. Thank you for your help!

Homework Statement For every ε> 0, there is a δ> 0 such that 1- δ< x <1 + implies 2- ε <7-5x <2 + ε Homework Equations The Attempt at a Solution My understanding of epsilon-delta proofs is very minimal at this point. Was hoping someone would be able to explain your thought...

Wow, the example of using fruit really helped clarify it a lot more. Thank you so much!

My mistake, it is an "if then" statement.

Homework Statement Hey guys! I am new to this forum but saw the helpful posts on set theory proofs and wondered if I could finally get some help with this problem: Suppose A, B, C, and D are sets with A⊆C and B⊆D. If A∩B=Ø then C∩D=Ø. This is a biconditional so I have to prove it...

Oh my mistake!

Hey guys! I am new to this forum but saw the helpful posts on set theory proofs and wondered if I could finally get some help with this problem: Suppose A, B, C, and D are sets with A⊆C and B⊆D. If A∩B=Ø then C∩D=Ø. This is a biconditional so I have to prove it both ways correct...