calc: Infinite Mode
7.4.4 Infinite Mode
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The Calculator normally treats results like ‘1 / 0’ as errors; formulas
like this are left in unsimplified form. But Calc can be put into a
mode where such calculations instead produce “infinite” results.
The ‘m i’ (‘calc-infinite-mode’) command turns this mode on and off.
When the mode is off, infinities do not arise except in calculations
that already had infinities as inputs. (One exception is that infinite
open intervals like ‘[0 .. inf)’ can be generated; however, intervals
closed at infinity (‘[0 .. inf]’) will not be generated when Infinite
mode is off.)
With Infinite mode turned on, ‘1 / 0’ will generate ‘uinf’, an
undirected infinity. 
Infinities, for a discussion of the
difference between ‘inf’ and ‘uinf’. Also, ‘0 / 0’ evaluates to ‘nan’,
the “indeterminate” symbol. Various other functions can also return
infinities in this mode; for example, ‘ln(0) = -inf’, and ‘gamma(-7) =
uinf’. Once again, note that ‘exp(inf) = inf’ regardless of Infinite
mode because this calculation has infinity as an input.
The ‘m i’ command with a numeric prefix argument of zero, i.e., ‘C-u
0 m i’, turns on a Positive Infinite mode in which zero is treated as
positive instead of being directionless. Thus, ‘1 / 0 = inf’ and ‘-1 /
0 = -inf’ in this mode. Note that zero never actually has a sign in
Calc; there are no separate representations for +0 and -0. Positive
Infinite mode merely changes the interpretation given to the single
symbol, ‘0’. One consequence of this is that, while you might expect ‘1
/ -0 = -inf’, actually ‘1 / -0’ is equivalent to ‘1 / 0’, which is equal
to positive ‘inf’.
Info Catalog
calc: Fraction Mode
calc: Calculation Modes
calc: Symbolic Mode