Re: Non-zero gaps between real numbers

On Dec 3, 6:18 am, William Hughes <wpihug...@xxxxxxxxxxx> wrote:
On Dec 2, 7:51 pm, Venkat Reddy <vred...@xxxxxxxxx> wrote:

Proove that the sum of measures of all real numbers in [0, 1] is equal
to 1.

The sum of all measures of all the real numbers in [0,1] is zero.
The measure of the set of real numbers in [0,1] is one.
The measure of the set of real numbers in [0,1] is not the sum
of all measures of the real numbers in [0,1].

That helps.

I guess it follows from the definition for measure? If it is not sum,
then what is it? Does that mean the measures of the sets [x,x] 0<=x<=1
have no role, or ccan't be related to the measure of [0,1] ?

Then is it equivalent to saying that points have no role in building
up the extent of a line segment, and hence line is not composed of
points?

- venkat
.

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