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Topic: Why do we need those real non-constructible numbers?
Replies: 4   Last Post: Nov 9, 2017 11:54 AM

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 wolfgang.mueckenheim@hs-augsburg.de Posts: 3,333 Registered: 10/18/08
Re: Why do we need those real non-constructible numbers?
Posted: Nov 9, 2017 11:43 AM

Am Donnerstag, 9. November 2017 10:43:42 UTC+1 schrieb John Gabriel:
> On Thursday, 9 November 2017 04:10:42 UTC-5, WM wrote:
> > Am Donnerstag, 9. November 2017 09:52:09 UTC+1 schrieb John Gabriel:
> > > On Thursday, 9 November 2017 01:45:55 UTC-5, WM wrote:
> > > > Am Donnerstag, 9. November 2017 00:20:12 UTC+1 schrieb John Gabriel:
> > > >
> > > >

> > > > > In fact WM, if you try to state that half itself or any other portion of itself measures it, then you've already assumed that the whole has a measure. That's incorrect.
> > > >
> > > > I assume that the diagonal of a square has a length.

> > >
> > > Of course a diagonal has a length, but it has no measure.
> > >
> > > Length =/= measure
> > >

> > Here you are a greater purist than me. But would it cause mathematics going astray when lenght is equated with measure of length and number is equated with measure?
>
> Well, I am surprised you even ask. Isn't that what is at the root of most discussions here on sci.math? How can you expect to have a clear discussion about mathematics when there is no agreement on what is the base concept, that is, *number* ?

There is a definition by majority decision. They call limits of Cauchy sequences real numbers.

Regards, WM