Contents of Checking Equality and Inequality

Checking Equality and Inequality

There are three possible responses to Check Equality: true, false, and undecidable . The latter means that the test is inconclusive and the equality may be either true or false. Maple and Mathematica use probabilistic methods to check equality, and there is a very small probability that an equation judged as true is actually false. Some expressions cannot be compared by this method—hence the inconclusive response.

$\blacktriangleright$ To check an equality

1.: Leave the insertion point in the equation.
2.: Choose Check Equality.

$\blacktriangleright$ Check Equality

e^iπ = - 1 is true

π = 3.14 is false

arcsinsin t = t is undecidable

You can also use Check Equality to check an inequality between two numbers. Set the difference of the two numbers equal to the absolute value of the difference, place the insertion point in the equation, and choose Check Equality.

$\blacktriangleright$ Check Equality

${\frac{{9}}{{8}}}$ - ${\frac{{8}}{{9}}}$ = $\left\vert\vphantom{ \frac{9}{8}-\frac{8}{9}}\right.$ ${\frac{{9}}{{8}}}$ - ${\frac{{8}}{{9}}}$ $\left.\vphantom{ \frac{9}{8}-\frac{8}{9}}\right\vert$ is true

π^e - e^π = $\left\vert\vphantom{ \pi ^{e}-e^{\pi }}\right.$ π^e - e^π $\left.\vphantom{ \pi ^{e}-e^{\pi }}\right\vert$ is false

These results verify that ${\frac{9}{8}}$ - ${\frac{8}{9}}$ ≥ 0, or ${\frac{9}{8}}$ ≥ ${\frac{8}{9}}$ ; and that π^e - e^π < 0, or π^e < e^π.

In most cases, you can recognize an inequality by inspection after applying Evaluate Numerically to each of the numbers.

$\blacktriangleright$ Evaluate Numerically

${\frac{{9}}{{8}}}$ = 1.125

${\frac{{8}}{{9}}}$ = .8888888889

π^e = 22.45915771

e^π = 23.14069264