Irrational Number

Author

Eric W. Weisstein
May 9, 2005

This notebook downloaded from http://mathworld.wolfram.com/notebooks/NumberTheory/IrrationalNumber.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/IrrationalNumber.html.

©2005 Wolfram Research, Inc. except for portions noted otherwise

Initialization

IrrationalQ[x_]:=!(x∈Rationals)

Known and unknown irrationals

$Version

l={Sqrt[2],Sqrt[3],E,Pi,Exp[Pi],2^Sqrt[2],Sin[1],Pi+Exp[Pi],2^E,Pi^E,Pi^Sqrt[2],EulerGamma,ProductLog[1]
};
TableForm[{#,IrrationalQ[#]}&/@l]

Sums

(∑_n^∞)((DivisorSigma[1, n])/(n!))

Sum[((DivisorSigma[1,n])/(n!)),{n,∞}]

NSum[((DivisorSigma[1,n])/(n!)),{n,∞}]

(∑_n^∞)((DivisorSigma[2, n])/(n!))

Sum[((DivisorSigma[2,n])/(n!)),{n,∞}]

NSum[((DivisorSigma[2,n])/(n!)),{n,∞}]