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Successor set

Revision as of 03:06, 26 January 2008 by Shreyas patankar (talk | contribs) (New page: A set <math>S\subset \mathbb{R}</math> is called a '''Successor Set''' iff (i)<math>1\in S</math> (ii)<math>\forall n\in S</math>; <math>n+1\in S</math> Note that the set of [[Natural ...)
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A set $S\subset \mathbb{R}$ is called a Successor Set iff

(i)$1\in S$

(ii)$\forall n\in S$; $n+1\in S$

Note that the set of natural numbers $\mathbb{N}=\{1,2,3\ldots\}$is not the only successor set.


For example, the set $S=\{1,\sqrt{2},2,1+\sqrt{2},\ldots\}$ is also a successor set.

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