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.)

-- 
                                                          - Warp

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