>>13765470>>13765554There's a number of reasons why pi=4 problem fails, but the most obvious to me conceptually is, as
>>13765607 said, analogous to the problem of determining the perimeter of coastlines:
>https://en.wikipedia.org/wiki/Coastline_paradoxThe problem is that the "jagged", square-like structure doesn't go away after a (countably) infinite number of iterations, so the "perimeter" doesn't actually converge on the circle, and you thus can't use induction in this way.
Basically, think of it as, the length of the "infinitely small" corners approaches zero, but the number of corners increases faster, so the "length" of these "corners" protruding from the actual circle ends up being greater than zero. I don't think this intuition works with "coastlines" in general, but it works here.
As far as the
>horse equivalence problemthere isn't any paradox, and the result R=Q=P is correct, merely by there being ANY intersection at all. It's not even an induction paradox in disguise, it's just set-theoretic.
