Difference between revisions of "Successor set"
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(ii)<math>\forall n\in S</math>; <math>n+1\in S</math> | (ii)<math>\forall n\in S</math>; <math>n+1\in S</math> | ||
| − | The set of [[Natural number|natural numbers]] <math>\mathbb{N}</math> is the '''smallest''' | + | The set of [[Natural number|natural numbers]] <math>\mathbb{N}</math> is the '''smallest''' successor set, as for any successor set <math>S</math>, <math>\mathbb{N} \subset S</math> |
Note that <math>\mathbb{N}=\{1,2,3\ldots\}</math>is not the only successor set. For example, the set <math>S=\{1,\sqrt{2},2,1+\sqrt{2},\ldots\}</math> is also a successor set. | Note that <math>\mathbb{N}=\{1,2,3\ldots\}</math>is not the only successor set. For example, the set <math>S=\{1,\sqrt{2},2,1+\sqrt{2},\ldots\}</math> is also a successor set. | ||
Revision as of 05:04, 26 January 2008
A set 
is called a Successor Set iff
(i)
(ii)
; 
The set of natural numbers 
is the smallest successor set, as for any successor set 
, 
Note that 
is not the only successor set. For example, the set 
is also a successor set.
