"lal_truckee" <[email protected]> wrote in message
> Ioannis wrote:
> > Neither can I
> > /really/ convince her that the set of primes is infinite. She relies on my
> > "credibility" to /believe/ this statement. She has no way to verify this
> > herself.
> If she can multiply and divide, she can understand the infinite primes
Well, she can certainly multiply and divide, but I would seriously doubt that
she can grasp the /mathematical/ meaning of "infinite". She's just a cute
mother afterall. Not a mathematician :-)
Anyway, I think most non-scientists understand the notion of "infinite" (if
they do, at all) from a more philosophical point of view, as a "tag" or
"placeholder/name" for something without bounds, or something /very very/ big.
Since empirical evidence outside mathematics for the existence of anything
with the "property" infinity does not really exist, fully understanding the
/mathematical/ notion of "infinite", which is ultimately an abstract mental
concept, I think requires a dedicated mathematical mind and considerable
experience. And even then, I am not 100% sure that ALL mathematicans out there
can actually grasp the notion without considerable effort. And then, even
/more/ effort is required when the mathematican understands that there are
even different kinds of infinity. But this raises a whole can of worms, which
quickly becomes OT, so I won't address it. To conclude: My mother /definitely/
cannot understand the notion of mathematical infinity, so she cannot possibly
understand the infinity of primes proof.
> - it's a very simple, elegant proof. "One from the book."
At least one more amateur astronomer here knows Erdos (and Euclid) :-)
The best way to predict reality, is to know exactly what you DON'T want.