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Topic: Defining the "number" correctly.
Replies: 1   Last Post: Nov 8, 2017 2:13 PM

 Me Posts: 1,716 Registered: 1/23/16
Re: Defining the "number" correctly.
Posted: Nov 8, 2017 2:13 PM

On Wednesday, November 8, 2017 at 8:51:45 AM UTC+1, John Gabriel wrote:
> On Tuesday, 7 November 2017 21:22:31 UTC-5, Me wrote:
> >
> > Moreover you are using the notion of limit in disguise when stating
> > "As n -> oo the sum of the columns becomes ..." etc.
> >

> Your birdbrain is brainwashed to think of limit, but the idea of LUB was
> around long before limit and calculus.

Of *WHAT*?! LUB, the /least upper bound/?

Holy shit! You know, the _LUB property_ holds *in the context of real numbers* - but not in the context of the rational numbers. (Hint: That's why each and every Cauchy sequence has a limit.)

https://en.wikipedia.org/wiki/Least-upper-bound_property

Actually, the LUB is QUITE CLOSELY related to the notion of limit, you know:

"If a sequence of real numbers is increasing and bounded above, then its supremum (LUB) is the limit."

> As n -> oo has ZERO to do with infinity. It means as n becomes indefinitely
> large,

*lol* n e IN certainly NEVER becomes "indefinitely large", after all there are no "infinitely large numbers" in IN.

> there is a limit.

Oh thanks, that made my day! :-)

You know my claim just WAS that "you are using the notion of /limit/ in disguise when stating 'As n -> oo the sum of the columns becomes ...'"