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.

>>> 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?

>> Graph
>> coloring problems don't necessarily have a consistent number of borders.
>
> True...
>
>>> But if you have a small mass, why would it be crushed to a small size?
>>
>> An incredible amount of force acted upon that mass?
>
> Oh. You mean something *outside* the mass itself causes it to become a
> black hole?
>
> But then, wouldn't that just mean that as soon as you remove the force,
> it wouldn't be a black hole any more?
>

Which is why a small black hole would be short lived. But, then, it does 
have an event horizon, and nothing can escape a black hole. So, wouldn't 
it remain a black hole after being compacted?

>>> But the speed of sound is /not/ constant. It changes depending on the
>>> motion of the source and the receiver. Light, on the other hand, has the
>>> seemingly impossible property that the relative motion of source and
>>> receiver somehow makes no difference to the apparent velocity of the
>>> light... but somehow *does* affect its wavelength? WTF?
>>
>> For the purposes of Doppler shift, it has a constant rate in the medium
>> it is in. The actual speed the waves move through the medium doesn't
>> change. The /relative/ speed does change, however. And is the same for
>> light. Sure, the relative speed of light can even be superluminal.
>
> No, it cannot.
>

Right, what was I thinking. Only the frequency of the light changes. The 
speed doesn't change.

>> Umm, to keep track of what's in your account? I generally do reconcile
>> my bank statement to my register (I keep mine electronically, so it's
>> fairly simple to do)
>>
>> I think this is basic home finance 101.
>
> Wait - you actually use a sophisticated electronic accounting package
> just for your home finance?
>

Heck no. Just a basic home finance program. Cost about US$50.

>>> A "root" is generally a part of a plant. Whereas a "route", as in, "this
>>> is how you get to this square number", would logically make more sense.
>>
>> Isn't the root considered the base of something? A Plants roots are at
>> its base, for example. for example the root word of unbelievable is
>> believe. You wouldn't say route in that context, would you?
>
> Hmm, I suppose...
>
Glad you see things my way for a change ;)

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