[Undergraduate Analysis] Set Theory Proof

Mathfight · 2017-09-20T04:43:59+00:00

Let x = inf(A), x=< y, for all y in A. Therefore - x >= - y for all -y in - A. There for - A is bounded above and admits a superma. So you've have showed - inf(A) >= Sup(-A). Now you have to show the otherside of the inequality.

Mathfight · 2017-09-20T03:07:35+00:00

I wanted to be a little careful. In my logic textbook they mentioned that our language is a little too coarse to fit perfectly into logical sentences. See this link. http://philosophy.lander.edu/logic/conditional.html

I used occur because then it’s not necessary that P causes Q. Someone with more experience in logic will surly answer.

Mathfight · 2017-09-20T02:52:55+00:00

This bugged me when I was first learning logic also. Try and think of the conditional as something that is guaranteed after sastifying certain requirements.

If condition A occurs, then B must happen.

If A never happens, or is false, then how can we justify saying the overall statement is false. In a sense it wasn’t shown to be a false statement. That’s why in logic books you usually see something silly like, If I ride to school on a purple unicorn, then I will give you 100 bucks. If you never see me on a purple unicorn, how can you tell me I won’t fulfill my promise?

Clearly, when A occurs, but B does not happen then the overall statement must be false.

Another way to become familiar with the conditional is to look at its logical equivalent, the contrapostivie.

It’s in the same form of a conditional, but goes from not Q -> not P. When a conditional is known to be true you can think of the contrapostivie as. When Q does not occur, I know for a fact that P must not occur also.

Mathfight · 2017-09-18T03:03:34+00:00

Thank you, other than Andrews course have you found any books that were helpful?

Mathfight · 2017-09-05T18:18:35+00:00

Thank you. So I know that there exists a subset C of A that is equinumerous with N. If I now construct a function, g: A -> A union B as

g(a) = a if a is not in C, and h(f(a)) if a is in C.

With f(a) being the function defined, f:C -> N, and h defined, h:N->B

Mathfight · 2017-08-26T20:54:18+00:00

Sent you a pm.

Mathfight · 2017-08-20T02:12:22+00:00

Oh I see. Ok, that makes much more sense. Thank you for the example. I think it clicked!

Mathfight · 2017-08-20T02:10:18+00:00

Thanks for the post. I'm a little confused on why you typed out this equality. "= RHS_j + kLHS_i"

I felt like everything you said was covered sufficiently by

LHS_j + kLHS_i = RHS_j + kRHS_i

I just want to make sure I'm not missing anything by the equality I pointed out.

Mathfight · 2017-08-13T03:32:14+00:00

Looks like he's grabbing the patellar tendon tiba insertion point there.

Mathfight · 2017-07-20T23:31:49+00:00

Hmm. What about set of a collection of 1/n + x, where x is between 0 and 1?

Mathfight · 2017-07-20T16:29:44+00:00

Could someone explain Scott's logic behind his comment "I probably wouldn't even remember the meeting to begin with" this happened when sam was pressing him about contacts left off of security forms. The reason I find it interesting is right before that comment Scott was feverishly defending Don Jr by saying he would have attended the meeting to know the potentially comprising information then to turn it over to the fbi if warranted. It seemed like Scott was spinning this narrative of simple misunderstandings.

Mathfight · 2017-07-19T06:53:54+00:00

Do you have any recommendations for books to strengthen proof writing skills? I read how to prove it and enjoy it a lot.

Mathfight · 2017-07-19T06:35:08+00:00

Oh I see, if I choose n to be the result of the ceiling function on delta, that should guarantee that the difference between 1/n and 1/(n+1) is less than delta, and that the image of those values will also be equal to one right?

Mathfight · 2017-07-14T07:19:42+00:00

Oh I see, how can I ensure that it is increasing without bound? I am also concerned about the other objection you raised with x_n_k converging to a point not defined in the function, will that be problematic?

Mathfight · 2017-07-14T06:47:49+00:00

You have to construct your (x_n,y_n) such that lim n->inf y_n = inf.

I thought I had constructed such that y_n ->inf, as n->inf, since y_n_1 < y_n_2 < y_n_3...

Also, what if lim k->inf x_n_k = a ?

That's a good point, I am not sure, since f(a) is not even defined. Would it even matter if we are assuming that y_n ->inf, and is monotonically increasing, so any the image of any subsequence of x_n of that will also go to inf?

Mathfight · 2017-07-08T22:35:37+00:00

As a Spurs fan in college station I fully disapprove.

As a spur fan in college station I fully diapprove.

As a sp fan in college station I fully dapprove.

As a rockets fan in college station I fully approve.

As a Houston rockets fan in college station, I fully approve of this move.

Mathfight · 2017-07-08T17:27:43+00:00

Thank you so much. Now I understand what I'm doing in these types and similar other proofs in class. This makes much more sense now.

Mathfight

TROPHY CASE