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SolveAsAStepOfAnUnboundedArgument​(AngouriMath.​Entity,​AngouriMath.​Entity.​Variable)

 Method (no overloads)

Summary

A step function of an unbounded argument times a factor that vanishes: the limit of
f * floor(g) is the limit of f * g, and the same for ceil and
round.

Remarks

floor(g) = g - r with 0 <= r < 1 wherever g is real, ceil(g) = g + r with the same bound, and round(g) is within 1/2 of g. So
f * floor(g) - f * g is f times something bounded by 1, which tends to 0
wherever f does, and the two products have the same limit, a value or an
infinity alike. Assumed, and checked: g is real-valued, and the other factors
tend to 0. Nothing is assumed of g's limit, which is the point -- the descent
puts each part's own limit in place of the part, so x floor(2/x) at 0 was read
as 0 * floor(+oo), a form it cannot settle, where it is 2 from either side.
Only a limit is taken from it. A NaN for f * g would say the same of the
step, but inside the machinery NaN can also be a form nothing read, so it is left
to the rules that already decide those.

























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