The principle of mathematical induction is a very very useful tool in many proofs, and also in proving some useful formulas. has ALL natural numbers if it follows the following conditions -
The first natural number, i.e. is in the set.
Whenever the integer is in the set, then is also in the set.
This looks so obvious, see that if you have been given the two statements simultaneously, then by using on , you can say that is in the set. Then again applying the statement for , we say that will be in the set, so on.
, for , just prove that it is true for and you're done !
Same thing you can do for 0, then prove for whole numbers !!!
Problems for practice:-
Prove that the following results hold
I felt like sharing because though it's very well known to all, I am willing to find some good level problems for practicing this foundation builder concept once more...