Recent content by INdeWATERS

Proof: Suppose, by way of contradiction, that this is not true. Then there exists a real number s such that both ar+s and ar-s are rational. I still don't see how to derive a contradiction. What should I choose s to be? Thanks for you help!

Use proof by contradiction to prove the following: Let a be an irrational number and r a nonzero rational number. Prove that if s is a real number, then either ar+s or ar-s is irrational. I am stuck with this proof. Here's what I have so far, Proof Suppose, by way of contradiction, that...

I am having issues with a proof, as follows. *U = universal set , P(U) = power set of a universal set For all sets A, B, C ∈ P(U), if A ⊆ C and B ⊆ C, then A ⊆ B or B ⊆ A. I am pretty sure the statement is false and so I have to disprove it, i.e. prove the negation. I am stuck on how to...

Also, how does my proof look for the original post? Prove set equality: (A-C) U (B-C) = (A U B) - C Proof: Show (A-C) U (B-C) ⊆ (A U B) - C and (A U B) - C ⊆ (A-C) U (B-C). Let A, B, and C be arbitrary sets. First, assume (A-C) U (B-C). Let x ∈ (A-C) U (B-C). Without loss of generality...

thank you for your help. Now, I am having issues with a different proof, as follows. U = universal set , P(U) = power set of universal set For all sets A, B, C ∈ P(U), if A ⊆ C and B ⊆ C, then A ⊆ B or B ⊆ A. I am pretty sure the statement is false and so I have to disprove it, i.e. prove the...

Thank you all for your help. It's greatly appreciated. I took some time to understand how the Flatten and Union commands work. Then, I approached my instructor about using them in my FareySequence code and I was, unfortunately, turned down. This FareySequence code is not meant to be efficient...

Thank you all for your help. It's greatly appreciated. I took some time to understand how the Flatten and Union commands work. Then, I approached my instructor about using them in my FareySequence code and I was, unfortunately, turned down. This FareySequence code is not meant to be efficient...

Unfortunately, I have never been introduced to how the Flatten[] and Union[] functions work. Therefore I can not use them. Is there some way I could use the Append[] function instead? Thanks for your time

Thank you for the help! I am in the process of writing up my proof... Is is possible to use the terminology "without loss of generality" in this proof? I know that involving that term can help me save a lot of writing... Thanks again

I need to prove the following: (A-C) U (B-C) = (A U B) - C I know that the union means that I have to do a proof by cases to show that these two sets are equal. But where do I start?! thanks

Here is an overview of Farey sequences; http://mathworld.wolfram.com/FareySequence.html" I need to write a program in Mathematica 8, FareySequence[n_], that takes a positive integer n and returns, as a list, the nth Farey sequence. So far I have, Module[{denleft, denright, f, i, j, k...

Wow! That totally works! But I was wondering if you could provide just a brief explanation of what each part of the code is actually doing... I am so new to programming and this code makes very little sense to me. Thank you very much for your time. triples[p_?PrimeQ] := Module[{out}...

Hello, I haven't attempted to put together a complete code just yet. I have the following so far; PythagoreanTriples[p_] := Module[{i, j, result, s, x, y}] s := Table[0, {j, 1, p-1)] result = {} I know I am missing A LOT of statements. But, like I said, I am very new to programming, and...

So, I am interested in finding solutions to the equation x^2 + y^2 = z^2 (mod p) where p is a given prime. For instance, if the prime were 17, then (6,8,7) is a PT mod 17, since 6^2 mod 17 = 36 mod 17 = 2, 8^2 mod 17 = 64 mod 17 = 13, 7^2 mod 17 = 49 mod 17 = 15, and 2 + 13 = 15. BUT! For...

Sorry, if (a,b,c) is a PT mod p, then so is (b,a,c). We consider all of these to be "equivalent." Thus, in listing PTs mod p, we make the restriction that a should be less than or equal to b, and both b and c should be less than p/2.