The type(x, infinity) function returns true if x is one of the following:

1.  infinity or -infinity

2.  a floating-point number whose exponent is infinity

3.  a nonreal of the form $a+\mathrm{I}b$, where at least one of a or b satisfies either (1) or (2)

Note: A nonreal is an expression of the form $a+\mathrm{I}b$, where b <> 0 and a (if present) and b are of type extended_numeric.

You can enter infinity using 1-D or 2-D math, as infinity or $\mathrm{\infty }$.

The type(x, cx_infinity) function returns true if x is written as y + I*z, where both y and z are of type infinity.

The type(x, real_infinity) function returns true if x is infinity, -infinity, or a floating-point number whose exponent is infinity.

The type(x, pos_infinity) function returns true if x is a positive real_infinity.

The type(x, neg_infinity) function returns true if x is a negative real_infinity.

The type(x, SymbolicInfinity) function returns true if x is either

1.  of type infinity

2.  a product with at least one factor of type infinity

A complex extended_numeric object in which one component is of type infinity and the other is of type undefined is considered to be of both types infinity and undefined.  In most computations, however, such an object is considered to be an infinity first, and an undefined second. See the last example below.

$\mathrm{type}\left(\mathrm{limit}\left(\frac{1}{x}\&comma;x=0\&comma;\mathrm{left}\right)\&comma;\mathrm{\infty }\right)$

$\mathrm{true}$

$\mathrm{type}\left(\mathrm{limit}\left(\frac{1}{x}\&comma;x=0\&comma;\mathrm{left}\right)\&comma;\mathrm{pos\_infinity}\right)$

$\mathrm{false}$

$\mathrm{type}\left(\mathrm{limit}\left(\frac{1}{x}\&comma;x=0\&comma;\mathrm{left}\right)\&comma;\mathrm{neg\_infinity}\right)$

$\mathrm{true}$

$\mathrm{type}\left(\mathrm{\pi }\&comma;\mathrm{\infty }\right)$

$\mathrm{false}$

$\mathrm{type}\left(a\mathrm{\infty }\&comma;\mathrm{\infty }\right)$

$\mathrm{false}$

$\mathrm{type}\left(\mathrm{I}\mathrm{\infty }\&comma;\mathrm{\infty }\right)$

$\mathrm{true}$

$\mathrm{type}\left(\mathrm{I}\mathrm{\infty }\&comma;\mathrm{cx\_infinity}\right)$

$\mathrm{false}$

$\mathrm{type}\left(2+\mathrm{I}\mathrm{\infty }\&comma;\mathrm{cx\_infinity}\right)$

$\mathrm{false}$

$\mathrm{type}\left(-\mathrm{\infty }+\mathrm{I}\mathrm{\infty }\&comma;\mathrm{cx\_infinity}\right)$

$\mathrm{true}$

$\mathrm{type}\left(\mathrm{limit}\left(\frac{1}{x}\&comma;x=0\&comma;\mathrm{left}\right)\&comma;\mathrm{SymbolicInfinity}\right)$

$\mathrm{true}$

$\mathrm{type}\left(\mathrm{I}\mathrm{\infty }\&comma;\mathrm{SymbolicInfinity}\right)$

$\mathrm{true}$

$\mathrm{type}\left(a\mathrm{\infty }\&comma;\mathrm{SymbolicInfinity}\right)$

$\mathrm{true}$

$\mathrm{type}\left(\mathrm{signum}\left(p\right)\mathrm{\infty }\&comma;\mathrm{SymbolicInfinity}\right)$

$\mathrm{true}$

$\mathrm{type}\left(-\mathrm{undefined}+2\mathrm{I}\&comma;\mathrm{undefined}\right)$

$\mathrm{true}$

x := Float(infinity + undefined*I);

$x≔Float\left(\mathrm{\infty }\right)+Float\left(\mathrm{undefined}\right)\mathrm{I}$

$\mathrm{abs}\left(x\right)$

$Float\left(\mathrm{\infty }\right)$

$\frac{1}{x}$

$0.+0.\mathrm{I}$