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Me
Posts:
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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


On Wednesday, October 4, 2017 at 12:43:52 PM UTC+2, genm...@gmail.com 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 "selfsupporting" (selfcontained)).
Hence I guess that you actually meant to write:
L = {x e Q : 1 < x < pi} and 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} and 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?



