Recent content by dirtybiscuit

  1. dirtybiscuit

    Constructing Nonlinear Well-Founded Orders

    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...
  2. dirtybiscuit

    Proof by Induction: Prove Fn-1Fn+1 - Fn = (-1)^n

    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.
  3. dirtybiscuit

    Proof by Induction: Prove Fn-1Fn+1 - Fn = (-1)^n

    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...
  4. dirtybiscuit

    Proof by Induction: Prove Fn-1Fn+1 - Fn = (-1)^n

    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...
  5. dirtybiscuit

    Proof by Induction: Prove Fn-1Fn+1 - Fn = (-1)^n

    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 -...
  6. dirtybiscuit

    Proof A U (A ∩ B) ⊆ A: Understanding x∈A

    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...
  7. dirtybiscuit

    Central Limit Theorem Question

    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...
  8. dirtybiscuit

    Calculating Probabilities for Sole Supplier Selection in Auto Industry

    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...