Inequality

Author

Eric W. Weisstein
April 14, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/Algebra/Inequality.nb.

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

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

Inititalization

<<Graphics`InequalityGraphics`
<<Algebra`InequalitySolve`

Two-dimensional Examples

|x-a|<b

InequalitySolve[Abs[x-a]<b,x]

Reduce[Abs[x-a]<b&&(a|b|x)∈Reals,x]

\[LeftBracketingBar]x-a\[RightBracketingBar]>b

InequalitySolve[Abs[x-a]>b,x]

Reduce[Abs[x-a]>b&&(a|b|x)∈Reals,x]

(x/y)>1

InequalitySolve[x/y>1,x]

Reduce[x/y>1&&(x|y)∈Reals,{x,y}]

Two-dimensional plots

ineq[i_,{x_,x0_,x1_},{y_,y0_,y1_},opts___]:=InequalityPlot[i,{x,x0,x1},{y,y0,y1},opts,DisplayFunction->Identity,PlotLabel->TraditionalForm[i], AxesLabel->TraditionalForm/@{x,y}]

Show[GraphicsArray[
{{
ineq[x>y,{x,-5,5},{y,-5,5}],
ineq[x/y>1,{x,-5,5},{y,-5,5}],
ineq[x^2+y^2<1,{x,-5,5},{y,-5,5}]
},{
ineq[Abs[x+y]<1,{x,-5,5},{y,-5,5}],
ineq[Abs[x] - Abs[y] ≤ 1,{x,-5,5},{y,-5,5}],
ineq[Abs[x] + Abs[y] ≤ 1,{x,-5,5},{y,-5,5}]
},{}}]]

Three-dimensional plots

Show[GraphicsArray[{
InequalityPlot3D[x^2+y^2+z^2<1,{x},{y},{z},PlotPoints->{15,40},Boxed->False,Axes->False,PlotLabel->TraditionalForm[x^2+y^2+z^2<1],
DisplayFunction->Identity],
InequalityPlot3D[x^2+y^2+z^2<1&&z<0,{x},{y},{z},PlotPoints->{15,20},Boxed->False,Axes->False,PlotLabel->TraditionalForm[x^2+y^2+z^2<1&&z<0],
DisplayFunction->Identity],
InequalityPlot3D[x^2+y^2-z^2<1,{x,-2.5,2.5},{y,-2.5,2.5},{z,-2.5,2.5},Boxed->False,Axes->False,PlotLabel->TraditionalForm[x^2+y^2-z^2<1],
DisplayFunction->Identity]
}]]