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seen Dec 14 at 18:42

Apr
21
answered Plotting a region in $3D$ space
Apr
21
comment Plotting a region in $3D$ space
Anyway, I just now notice that you specified a region in 2D ("$(x,y)\in\mathbb R^2$") with a parameter $z$. Did you possibly mean "$(x,y,z)\in\mathbb R^3$"?
Apr
21
comment Plotting a region in $3D$ space
Mathematica should be able to do that (with RegionPlot3D). However given that you tagged your question with maple I'm not sure that this answers your actual question (although it answers the question you've written).
Apr
21
accepted Non-constructive axiom of infinity
Apr
21
comment Is it possible that “A counter-example exists but it cannot be found”
OK, I changed that. Now OK?
Apr
21
revised Is it possible that “A counter-example exists but it cannot be found”
added 32 characters in body
Apr
21
comment Non-constructive axiom of infinity
Yes, that's the contradicton I mentioned. But where it the induction?
Apr
21
comment Non-constructive axiom of infinity
Hmmm ... with $A=\omega\cup\{\{42\}\}$ I get $\bigcup A=\omega\cup\{42\}\ne A$.
Apr
21
comment Non-constructive axiom of infinity
OK, I think I see now why your proof works, but I don't see where you use induction. As far as I can see you just build a contradiction by proving $\rank(\bigcup x)<\rank x$, which contradicts $\bigcup x=x$.
Apr
21
comment Non-constructive axiom of infinity
Ah, OK, that makes more sense. Now let me get back to understanding the rest. :-)
Apr
21
comment Non-constructive axiom of infinity
"We can prove that there are only finitely many sets of finite rank" ... but don't all natural numbers in the standard construction have finite rank? There are definitely infinitely many natural numbers (although each of them is of course a finite set in the standard construction).
Apr
21
comment n-dimension hypercube!
Duplicate? math.stackexchange.com/questions/763458/…
Apr
21
asked Non-constructive axiom of infinity
Apr
21
comment N-Dimension Hypercube question? (making sense of the question)
Are you sure you copied the complete text? Because it seems to me there's something missing (the grammar doesn't really work out well, either). I suspect the complete text contains something like "... to each of its vertex IDs and then we add new connections between pairs of vertices which differ only in the left-most bit."
Apr
21
comment Is it possible that “A counter-example exists but it cannot be found”
@TrevorWilson: Is the post now OK?
Apr
21
revised Is it possible that “A counter-example exists but it cannot be found”
Added a specific formalization to make the post correct
Apr
19
answered Visualizing the 48 actions of GL(2,3)
Apr
19
comment Is it possible that “A counter-example exists but it cannot be found”
@EricTowers: Actually the ordinal number version was exactly this interesting number paradox, with "natural" replaced by "ordinal" and "uninteresting" replaced by "undefinable". My point was that this paradox doesn't work with real numbers under the ordinary ordering, because other than non-empty sets of natural numbers, non-empty sets of real numbers (even bounded ones) don't need to have a minimum.
Apr
19
comment Is it possible that “A counter-example exists but it cannot be found”
@TrevorWilson: So the solution is to just demand a specific type of specification to be chosen, and then for this specific type of specification it is true? Or does the type of specification itself have to fulfil some requirements?
Apr
17
reviewed Approve how does this converges? Sequence and series convergence