Solution Found!
Solved: For exercise, use the fact that for all integersn,
Chapter 4, Problem 28E(choose chapter or problem)
For exercises 28 and 29, use the fact that for all integers n, n! = n(n − 1) . . . \(3 \cdot 2 \cdot 1\).
An alternative proof of the infinitude of the prime numbers begins as follows:
Proof: Suppose there are only finitely many prime numbers. Then one is the largest. Call it p. Let M = p! + 1.We will show that there is a prime number q such that q > p. Complete this proof.
Text Transcription:
3 cdot 2 cdot 1
Questions & Answers
QUESTION:
For exercises 28 and 29, use the fact that for all integers n, n! = n(n − 1) . . . \(3 \cdot 2 \cdot 1\).
An alternative proof of the infinitude of the prime numbers begins as follows:
Proof: Suppose there are only finitely many prime numbers. Then one is the largest. Call it p. Let M = p! + 1.We will show that there is a prime number q such that q > p. Complete this proof.
Text Transcription:
3 cdot 2 cdot 1
ANSWER:Solution:
Step 1:
In this question, we suppose there are only finitely many prime numbers. Then one is the largest be . Let
. We will show that there is a prime number q such that q > p.