The following is an incorrect proof of For every natural number n 1, in every group...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
The following is an incorrect proof of For every natural number n 1, in every group of n cars, all the cars are from the same state Proof by induction: Base case: In a group of 1 car, every car (i.e., that one car) is from the same state Induction step: Let n be an arbitrary natural number and suppose that in every group of n cars, all the cars are from the same state Consider a group of n+1 cars. By the induction hypothesis, cars 1 through n are from the same state and cars 2 through n+1 are from the same state Thus cars 1 through n+1 are from the same state This induction proof is obviously incorrect. What's wrong with it? The following is an incorrect proof of For every natural number n 1, in every group of n cars, all the cars are from the same state Proof by induction: Base case: In a group of 1 car, every car (i.e., that one car) is from the same state Induction step: Let n be an arbitrary natural number and suppose that in every group of n cars, all the cars are from the same state Consider a group of n+1 cars. By the induction hypothesis, cars 1 through n are from the same state and cars 2 through n+1 are from the same state Thus cars 1 through n+1 are from the same state This induction proof is obviously incorrect. What's wrong with it?
Expert Answer:
Answer rating: 100% (QA)
The incorrect part of the proof is in the induction step The error lies in the assumption that the f... View the full answer
Posted Date:
Students also viewed these mathematics questions
-
what do British Columbia's provincial authorities need to prioritize to enhance and convert the city of Vancouver into a world-class logistics hub? (five hundred words answer required) Introduction -...
-
In this question assume that p and q are atomic formulae. (a) Compare and contrast path formulae and state formulae in temporal logic. [4 marks] (b) Describe and contrast the meanings of F(G p) and...
-
Let A, B be sets. Define: (a) the Cartesian product (A B) (b) the set of relations R between A and B (c) the identity relation A on the set A [3 marks] Suppose S, T are relations between A and B, and...
-
Repeat the instructions of Exercise 1 for Graph the function Then discuss, in detail, limits, one-sided limits, continuity, and one-sided continuity of at x = -1, 0, and 1. Are any of the...
-
The total benefits of the COMMIT program which is designed to encourage school children to commit themselves to a life free of drug addiction has been estimated to be B = 800q - 4q2, where q is the...
-
A farmer has 100 lb of apples and 50 lb of potatoes for sale. The market price for apples (per pound) each day is a random variable with a mean of 0.5 dollars and a standard deviation of 0.2 dollars....
-
Alesch, Inc., manufactures goll clubs in three models. For the year, the Big Bart line has a net loss of \($10,000\) from sales \($200,000\), variable expenses \($180,000\), and fixed expenses...
-
If you put up $45,000 today in exchange for a 6.25 percent, 15-year annuity, what will the annual cash flow be?
-
Assets: $1,000,000 Liabilities: $300,000 Owner's Equity: $700,000 Sales: $800,000 Total Expenses: $500,000 What's the Return on Sales? 37.5% 62.5% 125% 42.857
-
A teacher believes that the third homework assignment is a key predictor in how well students will do on the midterm. Let x represent the third homework score and y the midterm exam score. A random...
-
Construct organizational training strategies that resolve emerging issues in a health care environment. : Demonstrate college-level communication through the composition of original materials in...
-
1) A loan of $8,600 is charged interest at 6.70% compounded semi-annually for the first 3.5 years, and then 5.20% compounded monthly thereafter. How much is owed at the end of 8 years? 2) A loan of...
-
You can use a calculator for these questions. Show your calculations. (a) Approximate the root of g(x) = 2 + x e^x between 1 and 2 to within 0.05 of the exact value using the bisection method. (b)...
-
1. What are some the topics from our course such as Kanban that have also been discussed in the management of the new decentralized system in UC Medicine's supply chain? Assignment Details: This...
-
8. The Bennet family consists of both parents, Tom and Jane, and the three children Rachel, Melissa, and Rob. When making major decisions like whether to go to Cape Cod again this year for vacation...
-
A quantity with an initial value of 5 1 0 grows exponentially at a rate such that the quantity doubles every 8 decades. What is the value of the quantity after 7 years, to the nearest hundredth?
-
A glass manufacturer produces hand mirrors. Each mirror is supposed to meet company standards for such things as glass thickness, ability to reflect, size of handle, quality of glass, color of...
-
Treasury Bonds. After the Global Financial Crisis especially, sovereign and portfolio investors from emerging market economies have purchased significant volumes of European treasury bonds. Discuss...
-
BOP and Inflation. What are the direct and indirect relationships between the balance of payments and inflation?
-
Capital MobilityEurozone. Low interest rates should normally lead to capital outflows to other countries and currencies in the search for higher interest rates. Explain why the opposite has occurred...
Study smarter with the SolutionInn App