eli5:if there’s an infinite number of triangles in a circle starting from Centrepoint to circumference then why cant we make up 2 circles in the real world from a single circle?

Question

eli5:if there’s an infinite number of triangles in a circle starting from Centrepoint to circumference then why cant we make up 2 circles in the real world from a single circle?

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Answer 1

If you are talking about copying an object as in the [Banach-Tarski paradox](https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox) – we say that we can’t do it because the proof of the paradox is non-constructive (and a constructive one cannot exist). We have no way of figuring out which points we would need to move to turn one circle into two circles, even if we had an imaginary machine that could select infinitely many infinitely small points and move them around. The proof simply says that such sets of points exist.