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dbpedia:Additively_indecomposable_ordinal	rdfs:label	"Additively indecomposable ordinal"@en .
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dbpedia:Additively_indecomposable_ordinal	dbpprop:abstract	"In set theory, a branch of mathematics, an additively indecomposable ordinal &alpha; is any ordinal number that is not 0 such that for any &lt;math&gt;\\beta,\\gamma&lt;\\alpha&lt;/math&gt;, we have &lt;math&gt;\\beta+\\gamma&lt;\\alpha. &lt;/math&gt; The set of additively indecomposable ordinals is denoted &lt;math&gt;\\mathbb{H}. &lt;/math&gt; Obviously &lt;math&gt;1\\in\\mathbb{H}&lt;/math&gt;, since &lt;math&gt;0+0&lt;1. &lt;/math&gt; No finite ordinal other than &lt;math&gt;1&lt;/math&gt; is in &lt;math&gt;\\mathbb{H}. &lt;/math&gt; Also, &lt;math&gt;\\omega\\in\\mathbb{H}&lt;/math&gt;, since the sum of two finite ordinals is still finite. More generally, every infinite cardinal is in &lt;math&gt;\\mathbb{H}. &lt;/math&gt; &lt;math&gt;\\mathbb{H}&lt;/math&gt; is closed and unbounded, so the enumerating function of &lt;math&gt;\\mathbb{H}&lt;/math&gt; is normal. In fact, &lt;math&gt;f_\\mathbb{H}(\\alpha)=\\omega^\\alpha. &lt;/math&gt; The derivative &lt;math&gt;f_\\mathbb{H}^\\prime(\\alpha)&lt;/math&gt; is written &lt;math&gt;\\epsilon_\\alpha. &lt;/math&gt; Ordinals of this form (that is, fixed points of &lt;math&gt;f_\\mathbb{H}&lt;/math&gt) are called epsilon numbers. The number &lt;math&gt;\\epsilon_0=\\omega^{\\omega^{\\omega^{\\cdot^{\\cdot^\\cdot}}}}&lt;/math&gt; is therefore the first fixed point of the sequence &lt;math&gt;\\omega,\\omega^\\omega\\!,\\omega^{\\omega^\\omega}\\!\\!,\\ldots&lt;/math&gt;"@en ;
	rdfs:comment	"In set theory, a branch of mathematics, an additively indecomposable ordinal &alpha; is any ordinal number that is not 0 such that for any &lt;math&gt;\\beta,\\gamma&lt;\\alpha&lt;/math&gt;, we have &lt;math&gt;\\beta+\\gamma&lt;\\alpha. &lt;/math&gt; The set of additively indecomposable ordinals is denoted &lt;math&gt;\\mathbb{H}. &lt;/math&gt; Obviously &lt;math&gt;1\\in\\mathbb{H}&lt;/math&gt;, since &lt;math&gt;0+0&lt;1."@en .
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	dbpprop:title	"Additively indecomposable"@en .
dbpedia:Additively_indecomposable	dbpprop:redirect	dbpedia:Additively_indecomposable_ordinal .