Difference between revisions of "Successor set"
(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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For example, the set <math>S=\{1,\sqrt{2},2,1+\sqrt{2},\ldots\}</math> is also a successor set. | For example, the set <math>S=\{1,\sqrt{2},2,1+\sqrt{2},\ldots\}</math> is also a successor set. | ||
| + | The set <math>\mathbb{N}</math> is called the [b]Smallest Sucessor Set[/b] because for any set <math>\mathbb{F}</math> that is a Succesor Set <math>\mathbb{N} \subset \mathbb{F}</math> | ||
| + | Also the set <math>\mathbb{N}</math> is calle dthe [b]Smallest Succesor Set[/b] because for any <math>\mathbb{F}</math> that is a succesor set <math>\mathbb{N} \subset \mathbb{F}</math> | ||
Revision as of 04:21, 26 January 2008
A set 
is called a Successor Set iff
(i)
(ii)
; 
Note that the set of natural numbers 
is not the only successor set.
For example, the set 
is also a successor set.
The set 
is called the [b]Smallest Sucessor Set[/b] because for any set 
that is a Succesor Set 
Also the set is calle dthe [b]Smallest Succesor Set[/b] because for any that is a succesor set
