Difference between revisions of "Successor set"

Revision as of 04:23, 26 January 2008

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. The set $\mathbb{N}$ is called the Smallest Succesor Set because for any $\mathbb{F}$ that is a succesor set $\mathbb{N} \subset \mathbb{F}$

@@ Line 9: / Line 9: @@
 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>
+The set <math>\mathbb{N}</math> is called the '''Smallest Succesor Set''' because for any <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>

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Difference between revisions of "Successor set"

Revision as of 04:23, 26 January 2008