Purchase Solution

Prove by contradiction that there does not exist a largest integer.

Not what you're looking for?

Ask Custom Question

Prove by contradiction that there does not exist a largest integer.
Hint: observe that for any integer n there is a greater one, say n+1. So begin the proof

"Suppose for contradiction that there is a largest integer. Let this integer be n...."

Purchase this Solution
Solution Summary

It is proven by contradiction that there does not exist a largest integer.

Solution Preview

Hello and thank you for posting your question to Brainmass.

Assumption:
N is the largest integer.

That is, for any ...

Purchase this Solution
Free BrainMass Quizzes
Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Probability Quiz

Some questions on probability

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

View More Free Quizzes
Related BrainMass Solutions

  • Divisors and relative primes

    But we stated beforehand that d does not divide into a, hence a contradiction (Symbolically represented by the opposing arrows).

  • Integer Proofs by Contradiction

    Use the proof by contradiction method to prove: (a) If 7n + 4 is an even integer, then n is an even integer. Proof. We prove it by contradiction. Suppose that n is NOT an even integer. Then n is odd. So, n=2k+1 for some integer k.

  • Show that 2006 is not the difference between two squares.

    We assume that we have the result for Problem 2. We prove by contradiction.

  • Showing a Residue System Modulo to a Prime Number

    Now, we are going to prove, for any , mod p NOTE: are NOT ZERO modulo p. We use method of contradiction. Suppose NOT, namely, for any , mod p where .

  • Hogatt's Theorem Proof

    Condition: Let n be the largest positive integer such that: First let's prove that : If Then This is a contradiction to the condition.

  • Ring Isomorphisms

    This is possible only if p(X)=1/2 and ½ does not belong to Z[X]. This contradiction proves that f cannot exist, so there is no isomorphism of rings between Z[X] and Q[X]. Ring isomorphisms are investigated.

  • Proofs : Circles and Irrational Numbers

    A circle has center (2, 4). 1. Prove that and are not both on the circle. 2. Prove that if the radius is less than 5, then the circle does not intersect the line given by . (Please give formal proofs for part 1 & 2.) II.

  • Proof by Contradiction: 3n + 2 is Even, N is Even

    424425 Use the proof by contradiction method. Assume that n is a positive integer. Use the proof by contradiction method to prove and explain if 3n + 2 is an even integer then n is an even integer.

  • Integer problems

    For any integer b in X, since b<=n, we can find some k such that kb is between n+1 and 2n. But this kb does not belong to Y. This means we can find x integers between n+1 and 2n.

View More Related Solutions