induction

robocop_911 · #1 $Old$ June 17th, 2008, 07:57 AM

Hi there,

I have a question...

When to take n = 0 (base case) and when to take n = 1 (base case) for proving statement P(n) by induction?

I've seen two-three examples some take n = 1 and some take n = 0.

kalagota · #2 $Old$ June 17th, 2008, 08:11 AM

some hints:

they often say: prove by induction that this statement is true for all $n\geq a$ ..

that $a$ becomes your base case..

more often than not, they say that the statement is true for all natural numbers, thus n=1 is your base.. (but others say it should be n=0.. however, by convention 0 is not a natural number)

EDIT: it just depends on what principle you use.. try reading Principle of Mathematical Induction

Reckoner · #3 $Old$ June 17th, 2008, 11:07 AM

Quote:

Originally Posted by kalagota $View Post$

but others say it should be n=0.. however, by convention 0 is not a natural number

What convention? I've heard many definitions that both include and exclude 0, and I am not aware of any general agreement.

kalagota · #4 $Old$ June 18th, 2008, 07:22 AM

Well, at least in our country (in particular in our university), most professors who had graduate studies in other countries, tell us zero is not included.

and it must be consistent to the fact that if zero is included (in the set N), then the set of whole numbers must be equal to the set of natural numbers. But, are they? And if they are, what is the sense of calling one on another name?

oh well, i maybe too young to debate on it. just ask your own professors about your local "convention". Ü