On 10/03/2011 02:37 AM, Mike Raiford wrote:
> On 3/8/2011 12:29 PM, Orchid XP v8 wrote:
>>>> It is undeniably infinite. But is it countable?
>>>
>>> Tell me when you're done counting from 0 to 1 in infinitesimally small
>>> intervals.
>>
>> "Countable" doesn't mean that you can actually count them in finite
>> time. It means that you can assign a unique positive integer to each one.
>>
>> Now, between 0 and 1 in the rationals, there are a countable infinity of
>> values. But in the reals (which inclused irrational numbers), there is
>> an uncountably infinite supply of values.
>>
>> So I suppose "how many points are there on the unit square" comes down
>> to "are the coordinates rational?"
>>
>
> Hmm... I don't have a strong enough grasp of number theory, apparently.

Set theory. Number theory is where you prove that irrational numbers 
exist. Set theory is where you prove that the set of irrational numbers 
has a strictly greater cardinal number than the set of rational numbers. 
And yes, transfinite cardinal numbers are freaking weird...

>>>> Sure. Regular Sudoku is 9x9. But you can make 'em other sizes (with
>>>> other numbers of unique symbols).
>>>
>>> Right, but, even if it were 25x25 it still has a specific layout.
>>
>> You can make them rectangular, you know. ;-)
>
> This would work? How?

http://en.wikipedia.org/wiki/Sudoku#Variants

>> Hmm, I suppose...
>>
> Glad you see things my way for a change ;)

Hey, I'm not *that* unreasonable. :-P

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