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Apr
23
comment What is the cardinality of $\bigcup_{n=1}^\infty\Bbb R^n$?
how can they be nested?
Apr
23
answered What is the cardinality of $\bigcup_{n=1}^\infty\Bbb R^n$?
Apr
23
comment Homeomorphism group
(+1) indeed :) :)
Apr
23
answered Homeomorphism group
Apr
22
comment hand evaluate $\sqrt{e}$
this limit expression for $e$ converges very slowly. Very very slowly.
Apr
22
comment hand evaluate $\sqrt{e}$
these converge quite slowly.
Apr
22
comment The automorphism group of the real line with standard topology
I need to think about this...
Apr
22
comment The automorphism group of the real line with standard topology
@OlivierBégassat yes, if you restrict to those homeos that fix a given point. Otherwise, there are too many reflections about each and every point. Also, some of the non-torsion elements may be too wild to deformation retract, I'm not sure. But certainly, there are too many 2-elements.
Apr
22
comment The automorphism group of the real line with standard topology
yes, I understand. My comment still stands. I think the topological structure is much more complicated.
Apr
22
comment The automorphism group of the real line with standard topology
@OlivierBégassat I think what you are describing is closer to what the group of homeomorphisms that fix $0$ would look like. I don't quite see where all the order $2$ elements (of which there are tons and tons of) and the elements of infinite orders would fit in your picture).
Apr
22
comment The automorphism group of the real line with standard topology
from the question, probably as a topological space.
Apr
22
comment Abelian isomorphic groups
well, if you are not clear why your argument is correct, then, no, you did not solve the problem.
Apr
22
answered Computer Science in mathematical setting
Apr
22
comment Abelian isomorphic groups
what is wrong???
Apr
22
comment Abelian isomorphic groups
any more information and I will be solving the problem entirely. Keep trying.
Apr
22
answered Abelian isomorphic groups
Apr
20
comment Are there contradictions in math?
@MarioCarneiro I can certainly agree with your interpretation (though I would not say that a mistake in a proof is a contradiction). But certainly we correct and improve as we go along (just like any other science following the scientific method). Contradictions (in whatever sense taken) are pushed out of relevant existence and as long as what remains is good, then we are happy. That is how science progresses.
Apr
18
comment Trigonometry Limit Question
the limit may be $\infty $, $-\infty $, or it may not exist. In fact, the limit of $\frac{1}{\sin x}$ as $x\to 0$ does not exist (and is thus not $\infty $).
Apr
17
comment Category , lie algebras …
(+1) for the answer and (+ million) for: "... more progressive in this regard than many since". Not only in Lie theory but also in other areas some of the more recent books are afraid to present even mildly categorical perspectives.
Apr
17
revised Are there contradictions in math?
added 1 character in body