The Paradox of the Mathematical Cone

Simon showed me an interesting paradox that’s difficult to wrap my mind around. If you slice a cone (at a random height), the section is a circle. The chopped-off part (a small cone) also has a circle as its base. Are those circles equal? They are the same, because they result from the same cross section. Hence the difference between them is 0. Now imagine slicing the cone an infinite number of times. “The difference between the circles will come up an infinite number of times: zero times infinity”, – Simon explained. “But zero times infinity has no value (or has any value, it’s indeterminate). Zero times infinity is the same as infinity minus infinity, which means that it can be whatever you want. Riemann’s rearrangement theory makes this true.”

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