Question

State the Division Algorithm for Natural number and prove it using induction

State the Division Algorithm for Natural number and prove it using induction

Homework Answers

Answer #1

Any doubt in amy step then comment below.. i will explain and clear ur all doubts okk..

Here we want to prove that remainder is less than q...

So we take two cases... Either (r+1) =q or (r+1) less than q ... And prove that in both cases , remainder comes out to be less than q...

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Using induction, prove the following: i.) If a > -1 and n is a natural number,...
Using induction, prove the following: i.) If a > -1 and n is a natural number, then (1 + a)^n >= 1 + na ii.) If a and b are natural numbers, then a + b and ab are also natural
Prove using induction that for any m,n is an element of natural number, if |{1,2,....,m}|= |{1,2,...,n}|...
Prove using induction that for any m,n is an element of natural number, if |{1,2,....,m}|= |{1,2,...,n}| then n=m
Prove by induction that if n is an odd natural number, then 7n+1 is divisible by...
Prove by induction that if n is an odd natural number, then 7n+1 is divisible by 8.
Using the method of induction proof, prove: If m and n are natural numbers, then so...
Using the method of induction proof, prove: If m and n are natural numbers, then so are n + m and nm.
Use strong induction to prove that every natural number n ≥ 2 can be written as...
Use strong induction to prove that every natural number n ≥ 2 can be written as n = 2x + 3y, where x and y are integers greater than or equal to 0. Show the induction step and hypothesis along with any cases
Prove by induction that if a and b are natural numbers, then a + b and...
Prove by induction that if a and b are natural numbers, then a + b and ab are also natural numbers.
Suppose we want to prove statement "Every even number squared is divisible by 4" using induction....
Suppose we want to prove statement "Every even number squared is divisible by 4" using induction. State and prove the base case.
Prove by induction. a ) If a, n ∈ N and a∣n then a ≤ n....
Prove by induction. a ) If a, n ∈ N and a∣n then a ≤ n. b) For any n ∈ N and any set S = {p1, . . . , pn} of prime numbers, there is a prime number which is not in S. c) Prove using strong induction that every natural number n > 1 is divisible by a prime.
Prove using induction: There is no rational number r for which r2=2.
Prove using induction: There is no rational number r for which r2=2.
9. Prove Euler's formula using induction on the number of vertices in the graph.
9. Prove Euler's formula using induction on the number of vertices in the graph.