Recent content by dirtybiscuit

Homework Statement My teacher has notes online that say: A Simple Construction Technique for WellFounded Orders Any function ƒ : S→N defines a wellfounded order on S by x < y iff ƒ(x) < ƒ(y). Example: Lists are wellfounded by length. Binary trees are wellfounded by depth, by number of nodes...

I made a mistake when I was typing. It should have said Fk+1(Fk - Fk+1) + F2k Then I used the defining relation on Fk+1 to get the next line.

Okay so this is what I got: Fk+1(Fk - Fk-1) + F2k Fk+1(Fk - Fk - Fk - 1) + F2k -Fk+1Fk-1 + F2k Multiply by -1 and get: Fk+1Fk-1 - F2k = -(-1)k+1 So P(k) = -(-1)k+1 The part about the -1 on the right hand side threw me off at the end but I think it makes sense. It seems unusual that this...

Thank you for your reply. With that I get: FkFk+2 - F2k+1 Fk(Fk+1 + Fk) - F2k+1 FkFk+1 + F2k - F2k+1 Fk+1(Fk - Fk+1) + F2k I'm not really sure where to go from this point. Just to verify that I am thinking of this the right way. I am trying to find a spot that I can use the assumption made...

Homework Statement The fibonacci numbers are defined by F0 = 0 F1 = 1 and Fn = n-1 + Fn-2 for n >= 2. Use induction the prove the following: Fn-1Fn+1 - Fn = (-1)n The attempt at a solution Let P(n) = Fn-1Fn+1 - Fn2 = (-1)n where n>= 1 Show it holds for first natural number: P(1) = F0 + F2 -...

Homework Statement I am trying to prove the absorption law A U (A ∩ B) = A I know that a way to prove this is to show that each is a subset of the other but I'm a little confused about one part in the process (below) Homework EquationsThe Attempt at a Solution Let x∈A U (A ∩ B) then x∈A or...

Homework Statement The Rockwell hardness of certain metal pins is known to have a mean of 50 and a standard deviation of 1.5. a)if the distribution of all such pin hardness measurements is known to be normal, what is the probability that the average hardness for a random sample of 9 pins is at...

Homework Statement Five companies (A,B,C,D and E) that make electrical relays compete each year to be the sole supplier of relays to a major automobile manufacturer. The auto company's records show that the probabilities of choosing a company to be the sole supplier are Supplier chain: A B...