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Topic: It is a very bad idea and nothing less than stupid to deny that
1/3 = 0.333...

Replies: 2   Last Post: Oct 1, 2017 11:29 PM

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jsavard@ecn.ab.ca

Posts: 403
Registered: 12/12/04
Re: It is a very bad idea and nothing less than stupid to define 1/3
= 0.333...

Posted: Oct 1, 2017 11:29 PM
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On Sunday, October 1, 2017 at 2:02:07 PM UTC-6, John Gabriel wrote:

> S = Lim S

> STOPS RIGHT HERE AND NOW. It is the Eulerian Blunder and has no place in
> rational thought, never mind mathematics.


S = Lim S isn't a statement of fact. It's a definition. It means that (in
certain appropriate cases) when we write an S that doesn't really have a
legitimate meaning, but Lim S does have a value, we are simply using S as a
shorter way of writing Lim S.

So we use this not as a way of saying that the bad, invalid, S is now a good
thing, but as a way of *getting rid* of S (and stuff like infinitesimals) and
_only_ using real things which do have values - such as Lim S.

You have just misunderstood what Euler was trying to do. He wasn't trying to
introduce bad messy thinking into mathematics; instead, he found some there, and
he was using this method to get _rid_ of all the messy stuff quickly without
having to make mathematicians do a lot of extra work.

Euler was not your enemy. He wasn't saying the false thing that S is just as
good as Lim S. He knew that S was bad, but Lim S was good, and he was therefore
doing just what you are trying to do: fix mathematics so that it rests on the
good stuff and doesn't try to use the bad stuff.

John Savard



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