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A new kind of infinitesimal
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Posted by: Steve Zimmerman
Describe a 135-degree angle.
On a horizontal plane, rotate the side of the angle that is orthogonal to the vertical (toward you would probably work better than away from you).
For every increment of rotation during this rotation describe whether or not the angle so described between the rotating leg and the non-rotating leg of the original 135-degree angle is indeed 135 degrees or 45 degrees.
The ambiguity of the time point so described between the time when the imaginary angle is 135 degrees and when it becomes 45 degrees is here technically defined as the infinitesimal.
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