On 3/7/2011 7:26 AM, Invisible wrote:
>>> The unit square contains an infinite number of points. But is it
>>> countably or uncountably infinite?
>>
>> I suppose you could say that it's an infinite set of all complex numbers
>> in the range of [0,1+1i)?
>
> It is undeniably infinite. But is it countable?
>

Tell me when you're done counting from 0 to 1 in infinitesimally small 
intervals.


> 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. Graph 
coloring problems don't necessarily have a consistent number of borders.

>
> 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?

>
> 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. And, 
light does travel at different rates in different media. C is simply the 
speed of light in a vacuum.

>>> Why do almost all species of birds bob their heads when they walk?
>>
>> Good question. I thought it was mostly just birds from the columbidae
>> family that did that.
>
> Seen a chicken walk recently? ;-)
>

Oh, right. I'm thinking columbidae is unique in how they can tuck their 
head ...

>
> Who the heck has an "account register" just for their personal stuff?
> For business expenses, sure. But just for, like, "I went to the corner
> shop yesterday and bought a loaf of bread", are you *really* going to
> check your bank statement to see if every single transaction like that
> was correctly charged? Who does this?
>

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.


>
> It's the "route" to that square.
>
>> Square root because it is the root of exponentiation operation.
>
> Which just means that the term is used elsewhere too.
>
> 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?



-- 
~Mike

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