Re:Imaginary numbers are real
by SideburnsOfDoom on Sunday July 24, 2022 @01:21PM
(#32215580)
Is that +∞ or -∞ though? The problem with division by zero is not that it's infinite, it is that it limit could be either +∞ or -∞ depending on which side of the limit you look at. Therefor, it is not well-defined.
[ Parent
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In some contexts +∞ = –∞ (e.g. tan ½π = tan –½π; these both represent the orientation of a line at a right angle).
In other contexts +∞ ≠ –∞ (e.g. log ±0 ≠ log ±∞; these quantities can be thought of as the two opposite ends of an infinite cylinder)
Re:Imaginary numbers are real
by SideburnsOfDoom on Monday July 25, 2022 @04:30AM
(#32221856)
Well, in that case the parent must ask themselves: am I doing geometry on an infinite cylinder or not?
For example, when you look at a world map under the Mercator projection and you want to know where the north and south poles should be on the map, the answer is +∞ and –∞, which are not the same.