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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?

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  • $\begingroup$ Did you mean $a_1=1$, at the begining, instead of $a=1$? $\endgroup$ – la flaca Oct 16 '16 at 23:36
  • $\begingroup$ 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}) $ $\endgroup$ – fleablood Oct 17 '16 at 2:40
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If you substitute p = n - 1, it may be clearer. Then you can index on p = 1,2,3...

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

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  • $\begingroup$ Thank you, indeed that helps. $\endgroup$ – Jebussy Oct 16 '16 at 23:39

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