So like, let's be clear This classic series: 1+1/2+1/4+1/8+1/16... Is, from a pure old-school POV, just as bad as the other one Even though this one looks like it has an answer (it adds up to 2 in the end)
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I think the plausibility of that falls down a little when you consider that the properties that distinguish the reals proper from, say, the analytic numbers, is _deeply weird_
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Like the fact that almost all of the real numbers can't even be described?
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The thing is that it feels to me like the integer are much more interesting than the reals. The reals are too smooth and have no structure while the integers are full of things like prime numbers which defy analysis by both having and not having structure at the same time.
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