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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Think of it like a preservation of mass in physics: if your circle is weighing 1ton, and you split it into 2, then both half will be weighing 0.5 tons, and there is no way around it. And even if you’re splitting indefinitely, if you keep track of the “weight” of each of the infinite triangles, then they must sum at 1ton.
Well, that’s a little more complex, since triangles that are infinitely small have weight “zero but not really zero”, so you need a more complex notion of measure to be able to talk about the weight of infinitely small triangles, but you can still do it.
In ELI5: instead of trying to weight a single infinitely small triangle, you never look at triangles alone and instead look at set of triangles and measure the weight of those sets.
But in the end, you still finish with the same issue: even if you split your infinitely many triangle into two infinities, by looking at their weight you will notice that the first infinity weight 1ton while the new infinity your created weight 0.5 ton each, so not enough to make two circles of the same size. (Though you could try to make two smaller circles, and then it become a much more complex problem)
[Small note: when you add a new notion to a problem that was not present before, like the weight here, you must check that this notion is compatible with everything you’re doing, otherwise you’re just cheating by adding constraints that weren’t there. And here “moving triangle around” will preserve the weight, so that’s fine. If you were to allow to scale-up or scale-down the triangles, then this “weight” argument would fall apart, but I’m assuming that in your question you were not allowing that.]
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