On 3/10/2011 3:24 AM, Invisible wrote:
> 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...
>

Ah. err... Got ya.

>>>>> 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
>

OK, aside from nonomino they all follow a pattern of n rows x n columns 
in blocks of n. nonomino changes this a bit by making the blocks 
arbitrary in shape.

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

Post a reply to this message