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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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 zelos.malum@gmail.com Posts: 1,176 Registered: 9/18/17
Re: Why do we need those real non-constructible numbers?
Posted: Nov 9, 2017 5:39 AM

Den torsdag 9 november 2017 kl. 10:43:42 UTC+1 skrev 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* ?
>
> Yes, mathematics has gone horribly off course - just look at all the junk concepts that have proliferated. I think it is time to re-examine everything - especially to make a return to the foundation of mathematics - geometry.
>
> Length is a concept like size or quantity. The measure of size or length or quantity is what results in a *number*. Of course we should be very precise in mathematics.
>

> >
> > Regards, WM

You mean like you whom choose to constnatly use words and sentences in ways that is NOT standard in order to make things more confusing?

Mathematics have gone exactly as it should, removing itself from the world and focus on abstracting things and being more general.

The issue of using such vague concepts is that they are vague and prone to be intepritated differently. By having it abstract into just sets, which follows logical rules only with no tie to our concepts, we remove that ambiguity.

BUt you wouldn't understand it as you thrive like a conartist by using vague language as if someone objects you will just go for another meaning of it. That is opposite of what mathematics does, it ties things down into very very strict definitions so that they can be properly argued about.