On 13/07/2013 5:44 PM, Warp wrote:
> Stephen <mca### [at] aolcom> wrote:
>> On 13/07/2013 2:50 PM, Warp wrote:
>>> 1) Does a unit square contain the same amount of points as a unit line?
>>> (We are talking about real numbers here.)
>
>> I would say no. They are different orders of infinity.
>
> You would have to explain that in more detail.
>
> Remember that, for example, one could easily think that there are "more"
> rational numbers than there are integers. Yet that's not correct. There
> are equally many. (That's because it's possible to construct a one-to-one
> relationship between every rational number and every integer.)
>
> If you can construct a function that gives a one-to-one mapping between
> the points on a unit line and the points on a unit square, that means
> that both sets have the same size (as unintuitive as that might sound.)
>

I got it wrong. It is not multiplying or raising the dimension that 
changes the size/order of an infinitive set. It is raising it by itself. 
E.g. multiplying the number of real numbers on a line by itself, 
itself's times. (Badly explained but I'm sure you can work out what I mean.)

I had a really bad journey yesterday, sitting on a grounded plane at the 
wrong airport for four hours. So I am not going to hurt my brain any 
more by reading about the perverted going ons of trans-infinities.

(If fractions were good enough for Alfred E Neuman then 11 dimensions, 
or is that 10, are good enough for me. :-) )

-- 
Regards
     Stephen

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