AngouriMath
IsIndeterminatePowerForm(AngouriMath.Entity,AngouriMath.Entity)
Method (no overloads)
Summary
Whether a power assembled out of the limits of its base and its exponent is an
indeterminate form that this library's arithmetic nonetheless answers with
a value, so that reading the value off would answer the limit wrongly.
indeterminate form that this library's arithmetic nonetheless answers with
a value, so that reading the value off would answer the limit wrongly.
Remarks
Substituting each part's own limit into a node and reading the result off is right
wherever the arithmetic is continuous there, and an indeterminate form is exactly
where it is not. Nearly all of them are already declined without any of this,
because they evaluate to NaN and every caller treats NaN as "no limit":
0 * oo , oo - oo , oo / oo and -- the one that matters here --
0^0 . That last is why lim x->0 x^x is NaN, which this library means
deliberately and pins inLimitTest.TestNoLimit , so 0^0 is **not**
listed here: declining it would turn a considered "does not exist" into "not
settled".
The gap is the two forms whose arithmetic gives 1 rather than NaN. oo^0 and
1^oo are each the shape of limits with different values -- (1 + 1/x)^x is e and 1^x is 1, both of them 1^oo -- and a limit that
assembled one of them read that 1 off as its answer:
lim x->+oo (x!)^(1/x) came back 1 where it is +oo.
This says nothing about what the expression (+oo)^0 evaluates to on its own.
That is a question of convention, on which this library agrees with SymPy and with
IEEE 754'spow in answering 1, and it is left exactly as it was.
#754
wherever the arithmetic is continuous there, and an indeterminate form is exactly
where it is not. Nearly all of them are already declined without any of this,
because they evaluate to NaN and every caller treats NaN as "no limit":
deliberately and pins in
listed here: declining it would turn a considered "does not exist" into "not
settled".
assembled one of them read that 1 off as its answer:
That is a question of convention, on which this library agrees with SymPy and with
IEEE 754's
#754
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