Difference between revisions of "Template:AotD"

Revision as of 13:49, 26 January 2008

Rational approximation of famous numbers

Rational approximation is the application of Dirichlet's theorem which shows that, for each irrational number $x\in\mathbb R$ , the inequality $\left|x-\frac pq\right|<\frac 1{q^2}$ has infinitely many solutions. On the other hand, sometimes it is useful to know that $x$ cannot be approximated by rationals too well, or, more precisely, that $x$ is not a Liouvillian number, i.e., that for some power $M<+\infty$ , the inequality [more]

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 <blockquote style="display:table;background:#eeeeee;padding:10px;" class="toccolours">
-===[[Power set]]===
+===[[Rational approximation of famous numbers]]===
-The '''power set''' of a given [[set]] <math>S</math> is the set <math>\mathcal{P}(S)</math> of all [[subset]]s of that set This is denoted, other than by the common <math>\math{P}(S)</math>, by <math>2^{S}</math> (which has to do with the number of elements in the power set of a... [[power set|[more]]]
+'''Rational approximation''' is the application of [[Rational approximation|Dirichlet's theorem]] which shows that, for each irrational number <math>x\in\mathbb R</math>, the inequality <math>\left|x-\frac pq\right|<\frac 1{q^2}</math> has infinitely many solutions. On the other hand, sometimes it is useful to know that <math>x</math> cannot be approximated by rationals too well, or, more precisely, that <math>x</math> is not a [[Liouvillian number]], i.e., that for some power <math>M<+\infty</math>, the inequality [[Rational approximation of famous numbers|[more]]]
 </blockquote>

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Difference between revisions of "Template:AotD"

Revision as of 13:49, 26 January 2008

Rational approximation of famous numbers