Quantum redactiones paginae "Numerus transcendens" differant

{{Tiro}}

'''Numerus transcendens''' vel '''transcendentalis'''<ref>[http://books.google.com/books?id=HUKtbIsjKucC&pg=PA334&lpg=PA334&dq=numeri+transcendentales&source=bl&ots=LDK56psSNE&sig=JyTdgHCdXXREIos5A_2QJ60nhWI&hl=en&ei=SWPdTajcBMPvsgb-v_HWBQ&sa=X&oi=book_result&ct=result&resnum=4&ved=0CC4Q6AEwAw#v=onepage&q=numeri%20transcendentales&f=false The triune God: systematics By Bernard J. F. Lonergan, Robert M. Doran, Daniel Monsour]{{ling|Latine}}</ref> est [[numerus]] [[numerus realis|realis]] vel [[numerus complexus|complexus]] qui [[Numerus algebraicus|algebraicus]] non est.

 

Sit <math> x \in \mathbb{R} </math> numerus transcendens. Tunc nullus est <math> n \in \mathbb{N} \setminus \lbrace 0 \rbrace </math> et nulli sunt <math> a_i \in \mathbb{Q} \ (0\le i \le n-1) </math>, ut <math> \sum_{i=0}^{n-1} {a_i \cdot x^i} + x^n = 0 </math> sit.

 

Confirmatum est certos numeros transcendentes esse possunt per argumenta [[1844|anno millesimo octigentesimo quadragesimo quarto]] ab [[Iosephus Liouville|Iosepho Liouville]] facta, qui genus numerorum transcendentum ([[Liouville numerus|Liouville numeri]]) construxit; inter his [[Liouville constans]] est:

<math>\sum_{k=1}^\infty 10^{-k!} = 0,110001000000000000000001000\ldots</math>