Tuesday, February 12, 2013
Proof by induction
Suppose we want to prove something is true about all the objects in a set. Let's say they were citrus
fruits. Statement:everycitrus fruit has a certain amount of vitamin C in the juice. You can prove this by
evaluating every fruit and showing that it is true for each. If the set is infinite however,you can't do that.
- Proof by induction is useful for proving statementsabout all membersof infinite sets.
- Provethe statementis true for the first member of the set
- Provethat if it is true for some member, it is also true for the next memberof the set.