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Topic: I rarely make silly mistakes, but Euler made a huge blunder in S
= Lim S

Replies: 4   Last Post: Oct 4, 2017 11:37 AM

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Posts: 1,716
Registered: 1/23/16
Re: I rarely make silly mistakes, but Euler made a huge blunder in S
= Lim S

Posted: Oct 4, 2017 11:37 AM
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On Wednesday, October 4, 2017 at 12:43:52 PM UTC+2, wrote:

> Even "Me" has finally understood that my definition is a D. Cut.

No, I haven't. Sorry about that.

But... you write:

> L={-1 < x < pi} and R={pi < x < 4} where x \in Q

Again, a rather "uncommon" notation (to say the least).

For example there seems to be a free variable, "x", in the expression "{-1 < x < pi}" (for example). Hence I don't think it qualifies for a "term" just denoting a "specific" set. Moreover you "externalize" the information that "x" ranges over all elements in Q; we usually put this into the "set terms" (such that they are "self-supporting" (selfcontained)).

Hence I guess that you actually meant to write:

L = {x e Q : -1 < x < pi}
R = {x e Q : pi < x < 4} .

Actually this corresponds to a quite natural way of referring to these sets.

For example, {x e Q : -1 < x < pi} is /the set of all elements in Q that are larger than -1 and smaller than pi/.

Now concerning Dedekind cuts, you might improve your approach by just defining:

L = {x e Q : x < pi}
R = {x e Q : pi < x} .

Then (L, R) would actually qualify for a "D. cut", I guess.

So why not choose the simpler approach?

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