Comments by "Christian Baune" (@programaths) on "Can You Upload Your Mind \u0026 Live Forever?" video.
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@ThatDangerousBacon If infinitesimals is a bit a spice, Cantor's proof is...milk 🤣
Here is a mind bender that shows how twisted is infinity and infinitesimal.
Go through each statement and decide if it's true or false, then draw your conclusion. You may be surprised. All True/False are bound to the Euclidean plane.
1) Two segments, whatever is their length (not infinite, otherwise it's a LINE), have the same number of points. This is shown by appropriately project on segment on the other.
2) An equilateral triangle has three equals sides. Hence, the sides have the same number of points (easy one!)
3) If we color points from a segment as such two neighbors do not have the same color and using to colors, extremities (first and last points) would be of the same color if the number of point is odd and of different colors if the number of points is even.
4) If we color points from a segment in an alternating fashion, point at the same distance from a center (circle) should have the same color.
5) In an equilateral triangle, lying implicitly on a circle, the 3 vertex have the same color
6) An equilateral triangle can fill the plane by growing, filling the plane with nested triangles, the trace of the vertex is of one unique color if one triangle vertex is fixed.
7) An equilateral triangle can be rotated and the vertex do not flip color (variation of 4)
8) The plane can only colored with one color.
Enjoy!
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