Recent content by Jaquis2345

Proof: Suppose f is a function and x is in the domain of f s.t. there is a derivative at the point x and sppse. there are two tangent lines at the point (x,f(x)). Let t1 represent one of the tangent lines at (x,f(x)) and let t2 represent the other tangent line at (x,f(x)) s.t. the slopes of t1...

After working on the problem for a while this is what I got (roughly). Since the point x is to the right of every point in the sequence, then from the completeness axiom there is either a rightmost point of the set contains all points of the sequence or a first point to the right of that set. I...

After emailing my professor it seems there was a typo in the problem we were given. I just need to show that the sequence converges not that it converges to x.

So far this is what I have. Proof: Let p1, p2, p3 be a non-decreasing sequence. Assume that not all points of the sequence p1,p2,p3,... are equal. If the sequence p1,p2,p3,... converges to x then for every open interval S containing x there is a positive integer N s.t. if n is a positive integer...

So no element of H can exist in the new interval other than possibly p. Thus, K exists in (a,b) and (c,d) where every point of K in that intersection is not equal to p. Right?

Summary: Definition: If M is a set and p is a point, then p is a limit point of M if every open interval containing p contains a point of M different from p. Prove: that if H and K are sets and p is a limit point of H ∪ K,then p is a limit point of H or p is a limit point of K In this proof I...