Testing random

[Ian Kelly]

On Jun 16, 2015 4:58 PM, "Ian Kelly" <ian.g.kelly at gmail.com> wrote:
>
> On Tue, Jun 16, 2015 at 4:30 PM,  <sohcahtoa82 at gmail.com> wrote:
> > On Tuesday, June 16, 2015 at 3:01:06 PM UTC-7, Thomas 'PointedEars'
Lahn wrote:
> >> This should give you pause: In real mathematics, events with zero
> >> probability can occur.
> >
> > Nobody will disagree with that.  The probability of me winning the
lottery is zero if I don't buy a ticket.
>
> I believe he's actually referring to this:
>
> https://en.wikipedia.org/wiki/Almost_surely
>
> Not that this has anything to do with the probabilities under
> discussion in this thread.

Actually, I take that back. The coin flip example in the Wikipedia article
is exactly what we've been discussing, taken to the ultimate extreme of an
infinitely long sequence.

Unfortunately for Thomas, the article does not agree with his position,
describing the event of never flipping a tail in such an infinite sequence
as "almost never". If, as Thomas maintains, the probability of this event
does not decrease as the length of the sequence increases, then the
probability for the infinite sequence would have to be non-zero since the
probability for any finite sequence is non-zero.
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