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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


On Sunday, October 1, 2017 at 2:02:07 PM UTC6, 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



