# Defining Elements By Induction

Can someone give insight into this?

'The elements in a set may be defined by a recursive or inductive rule. For example, consider the set of numbers {a1, a2, a3} where a=1,

an = an-1 + 1 for n = 2 or 3.

The elements are a1 = 1, And a2= a1 + 1= 1+1 = 2, And a3 = a2 +1 = 2+ 1= 3.

The an - 1 + 1, is what I don't understand. Am I to infer that n is zero, and 1 then becomes the first element?

• Did you mean $a_1=1$, at the begining, instead of $a=1$? – la flaca Oct 16 '16 at 23:36
• No. You are to infer $n$ is some number bigger than 1, and that n-1 is some number you have already dealt with (it could be 1) so that you have already figured out what $a_{n-1}$ is. This is just a way to define a list of terms. $a_1= something$ then you define $a_n$ for all $n>1$ as $a_n = some manipulation of (a_{n-1})$ – fleablood Oct 17 '16 at 2:40

For p=1, $a_p$ = 1, etc