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Originally Posted by xepherys
I would think, in it's context, that an anti-circle would, in fact, be all area not encompassed by said circle. It's equation would take all of existance and subtract from it the area of the known circle.
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To nitpick... a circle is defined as as set of points in a plane equidistant from a point. So an "anti-circle" would not necessarily have anything to do with the area inside a circle.
Running with the assumption of a circular area, though... what about non-cartesian geometry? A circle drawn on a spherical plane divides the surface into two areas... but both are circular.
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Originally Posted by xepherys
For something to be coined as an opposite, it must have some similarity.
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The best opposites are similar in all respects except for the characteristics you wish to illustrate. It's a way of saying "All these similarities are not significant." So Cat/Dog is a good set of opposites
because they're both furry animals, that live on earth, eat meat, are kept as pets, have tails, bear live young, have four feet, etc. If, however, you oppose platypus and freedom... it's not really clear what the hell you're trying to get at with the comparison (or the contrast, rather).