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.