[Tutor] Cantor pairing in three dimensions?

[Brian van den Broek]

On 24 December 2013 16:21, Brian van den Broek
<brian.van.den.broek at gmail.com> wrote:
> On 23 December 2013 13:32, Danny Yoo <dyoo at hashcollision.org> wrote:
>>
>> I've got a puzzle: so there's a well-known function that maps the
>> naturals N to N^2: it's called Cantor pairing:
>>
>>     http://en.wikipedia.org/wiki/Pairing_function

<snip>


> Hi Danny,
>
> It does generalize; a well known result of set theory has it that the
> Cartesian product of finitely many countable sets is itself countable
> (where countable means either finite or infinite but able to be mapped
> 1:1 to the natural numbers). Here's a hand-wavy proof sketch that
> assumes we've already got the map N -> N^2:

<snip me blathering wrongly>


Hi Danny and all,

What I said was not right. (I cannot now see how I thought it was.) Apologies.

For an actual proof:
http://planetmath.org/thecartesianproductofafinitenumberofcountablesetsiscountable.

Best,

Brian vdB