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Topic: Weierstrass
Replies: 26   Last Post: Jul 9, 2004 4:27 PM

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Herman Jurjus

Posts: 447
Registered: 12/6/04
Re: Weierstrass
Posted: Jul 8, 2004 10:59 AM
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Eckard Blumschein wrote:
> Someone wrote: ... [1.5 , 2.5)
> (where 1.5 and 2.5 are 'infinite-precision' numbers...)
> Does nobody share my reluctance to distinguish between
> included and excluded infinite-precision numbers?


Sure; cf. Hjlemslev.
But perhaps it is best to dig somewhat deeper.

Let us forget, for a moment, these infinite
precision numbers. Let's say, we have (or want
to have) a number system that contains only
your 'interval-like' numbers. So, for example,
there exist numbers like 0.27 and 0.270, but
these numbers are different (contrasting with
the usual system).
Now i suppose you may want to define some special
relation between these numbers, namely something
like ' 0.27 is an approximation of 0.270 ',
or '0.270 is a precization of 0.27 '.
Is that still along your line of thoughts?

Now, would you like to say that, eg.,
0.27 approximates 0.27499
and it also approximates 0.27499999 and also 0.274999999999, etc.
but that 0.27 does not approximate 0.275, nor 0.2750, etc. ?

Or do you want something more subtle than that?

> I am not Buridan's donkey.

Neither is any of us (i suppose), thank you.
Can you explain what relevance you see for
that old story in this discussion?
What are the two things that modern mathematics
fails to choose from, and what does it miss,
because of that?

--
Cheers,
Herman Jurjus




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