Uergil
Posts:
433
Registered:
6/11/11
|
|
Re: WMatheology ? 047
Posted:
Jun 28, 2012 2:34 AM
|
|
In article <4FEB701C.9AC41B33@btinternet.com>,
Frederick Williams <freddywilliams@btinternet.com> wrote:
> Uergil wrote:
>
> > If y is a point "next to" x, where does (x + y)/2 lie?
>
> I find that sort of thing quite unconvincing. If WM claimed that there
> was a next integer after 3, viz 4; and you asked where does (3 + 4)/2
> lie? He could reasonably reply, either: There is no such thing as (3 +
> 4)/2, I.e. there is no such integer. Or, (3 + 4)/2 lies at 3.5.
But both the set of rational numbers and the set of real numbers, with
their arithmetics, form ORDERED FIELDS, and, in any such field, if x and
y are different, then (x+y)/2 exists and is between x and y.
--
"Ignorance is preferable to error, and he is less
remote from the- truth who believes nothing than
he who believes what is wrong.
Thomas Jefferson
|
|
