Thread: Strong Induction

We are starting a topic of "Strong Induction", but I don't see the difference between it and the regular induction that we did a few months ago. What's the difference?

Originally Posted by English Major

We are starting a topic of "Strong Induction", but I don't see the difference between it and the regular induction that we did a few months ago. What's the difference?

In ordinary induction you prove n+1 using n but in strong induction you prove n using all k<n. So for example, we will prove every number n>=2 is a product of prime. Suppose it is true for all k<n we will prove it is true for n. If n is prime proof complete. Otherwise n=p*q where p,q<n but by strong induction p and q are a product of primes, so n is a product of primes.