Zero

Author

Eric W. Weisstein
October 26, 2005

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Numbers/Zero.nb.

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

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

(0^0)

Plot

<<Graphics`Colors`

Plot[Evaluate[Table[a^x,{a,.2,2,.2}]],{x,0,2},PlotStyle->List/@{Red,OrangeRed,Orange,Yellow,Green,LightBlue,Blue,Indigo,Violet,Purple},AxesLabel->TraditionalForm/@{x,a^x}]

Evaluation

0^0

0^0.

0.^0

0.^0.

FullSimplify[0^n,n∈Integers]

0^n

n^0

ComplexExpand[a^(x+I y)]/.a->0

ComplexExpand[0^x]

FullSimplify[0^(x+I y),Element[(x|y),Reals]]//InputForm