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Topic: Matheology § 062
Replies: 181   Last Post: Jul 14, 2012 1:48 PM

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 Virgil Posts: 8,833 Registered: 1/6/11
Re: Matheology � 062
Posted: Jul 13, 2012 3:47 PM

In article
WM <mueckenh@rz.fh-augsburg.de> wrote:

> On 13 Jul., 10:17, Virgil <vir...@ligriv.com> wrote:
>

> > On the contrary, in STANDARD mathematics, the arguments of a function
> > need not be numbers at all, but can be members of any set at all.

>
> In standard mathematics, the limit of the sequence (1/n) is 0 and only
> 0.

But a function discontinuous at each -1/n, as is the case here, need not
be continuous at 0.

The actual number of balls in the VASE function of time in seconds is
0 for t < -1,
9*n for -1/n <= t < -1/(n+1)
for all times before 0, so is increasingly discontinuous at each
t = -1/n ( the discontinuities keep getting larger as n increases),
a set of values converging to 0.

But now WM claims, as usual without proof, that that function MUST be
'sort of continuous' at an accumulation point of its discontinuities.
--

Date Subject Author
7/7/12 mueckenh@rz.fh-augsburg.de
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7/8/12 LudovicoVan
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7/8/12 William Hughes
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