Re: Cantor Confusion

In article <1161159542.523113.318440@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> mueckenh@xxxxxxxxxxxxxxxxx writes:

*** T. Winter schrieb:

In article <1161007554.513186.56640@xxxxxxxxxxxxxxxxxxxxxxxxxxxx> mueckenh@xxxxxxxxxxxxxxxxx writes:
...
> > > The function f(t) = 9t is continuous, because the function 1/9t is
> > > continuous.
> >
> > Yes, but that is not the number of balls in the vase.
> >
> For the t-th transaction 9t is the number of balls in the vase.

Let me clarify. WM apparently asserts that if a function g(x) is continuous
at some point, so is 1/g(x). That is (obviously) false. sin(x) is
continuous at x = 0, while 1/sin(x) is not.

I used but a simple definition of the improper limit oo of the function
x which is given by the fact that the function 1/x has the proper
limit 0 (fo x --> oo in both cases).

Let me ask. You *did* state that "The function f(t) = 9t is continuous,
because the function 1/9t is continuous", yes? Do you not see that that
reasoning is wrong? That if 1/f(t) is continuous that does not mean that
f(t) itself is continuous?

Moreover, when we let t go to infinity, 1/9t is *not* continuous at
infinity (whatever that may mean). We can only define the limit,
not the function value.

We can only define limits in *all* cases concerning the infinite.
Nothing else is possible.

Yes, so you can not talk about continuity.
--
*** t. winter, cwi, kruislaan 413, 1098 sj amsterdam, nederland, +31205924131
home: bovenover 215, 1025 jn amsterdam, nederland; http://www.cwi.nl/~***/
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