forceOfHabit
Sep 4, 2018 · 1 min read

Hi Mark,

The whole argument depends on being able to re-order terms. Its not that there’s anything wrong with that, its just that one should be aware that when dealing with the perplexities of infinity, that necessarily becomes an axiom, not just a consequence of commutativity as it would be for finite series of numbers. Otherwise you get other weirdness like proving 1 = 0 (as in the Riemann series theorem), or even just simple counting arguments. (e.g. its intuitively obvious there are twice as many positive integers as even positive integers. But if we take the sequence of positive integers and multiply them all by 2 we get the sequence of even positive integers. But multiplying every member of the sequence by 2 doesn’t change the number of members. So there are exactly the same number of positive integers as even positive integers. So which is it? Twice as many or the same number?)

    forceOfHabit

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