Re: Calculus XOR Probability

cbrown@xxxxxxxxxxxxxxxxx wrote:
Tony Orlow wrote:

So, I feel justified, until I see a good counterexample, that
equality between quantitative expresseions proven inductively hold in the
infinite case.

So, your idea of a mathematical argument is: n*(n+1)/2 is the sum of
the naturals from 1 to n, because you haven't seen a good
counter-example?

I think you are misreading Tony here. Tony is claiming that
because 1 + 2 + .... n = n*(n+1)/2 when n is finite, it is also
true when n is infinite, and he will continue to believe in
general that any equality that holds for the finite case
also holds in the infinite case until you provide a counter example
where it is clear that the equality does not hold in the infinite case.

Of course your stairstep example was meant to be exactly
that, but Tony does not see it that way, especially since
he has now decided that points have a "direction", although
he did admit that some points have multiple directions.

Stephen
.

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