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6h
comment minimal embeddings of topological spaces into connected spaces
...oh actually, you said a one-point compactification, not the one-point compactification. Never mind then. :)
6h
comment minimal embeddings of topological spaces into connected spaces
By the way, it isn't quite right to call this the one-point compactification of $X$. In a one-point compactification, the added point typically does have neighborhoods that aren't the whole space. It happens that the one-point compactification of $\mathbb Q$ is also connected, so it's another good example.
6h
comment minimal embeddings of topological spaces into connected spaces
In the terminology of Steen and Seebach's Counterexamples in Topology, this is the open extension of $X$. They also note that it is connected, as reflected at proofwiki.org/wiki/Open_Extension_Space_is_Connected
13h
comment How do we add numbers?
(Well, if a pile of rocks is considered an acceptable encoding of a number, then we can just lump the piles together with a bulldozer to compute the sum!)
1d
comment Determinant of symplectic matrix
@RSG Sorry, I've long since forgotten what little I once knew on the topic. :) You might want to raise another question with tag:reference-request for that.
1d
comment Determinant of symplectic matrix
For future reference, these are related questions without any constraints on the method of proof: math.stackexchange.com/questions/242091/… math.stackexchange.com/questions/501130/… math.stackexchange.com/questions/930319/…
1d
answered Determinant of symplectic matrix
1d
comment Combination of Variables
The question doesn't make much sense because it isn't clear what purpose the combinations are meant to fulfill. Could you please describe the larger problem you're tackling? For example, is there some objective function over combinations of 6 variables that you're trying to minimize, and you want to avoid performing a brute-force search over all 82 million combinations? If so, the form of the objective function might allow a massive simplification that reduces the search space. But we'll need to know what the objective function is, first.
1d
answered Squares in $\mathbb Z_p$
2d
answered Compact subsets of the space of real functions $\mathbb{R}^\mathbb{R}$
2d
comment Continuous function on compact subset of $\mathbb R$ to itself has a fixed point.
What is the title and edition of the textbook, and what is the page number of the proof? There are three errata listings for different versions of "A Course in Calculus and Real Analysis" at math.iitb.ac.in/~srg/acicara.
2d
comment Determining if a number is a prime
Where does the problem come from?
2d
comment Why Cantor set removes one third?
To be clear, Abbott uses the usual middle-thirds Cantor set throughout the book. The middle-fourths set is discussed only in Exercise 3.4.4.
May
25
revised Visualize $z+\frac{1}{z} \ge 2$
+visualization tag
May
25
answered Visualize $z+\frac{1}{z} \ge 2$
May
25
comment $\epsilon$-dense subsets on $\mathbb R/\mathbb Z$.
Is there a particular step that doesn't seem to work? Maybe I can help to bridge the gap.
May
25
answered $\epsilon$-dense subsets on $\mathbb R/\mathbb Z$.
May
24
comment The limit is that which is neither too big nor too small to be the limit.
Well, it has its advantages. One can talk about liminfs and limsups without uttering the phrase "if it exists" every ten seconds, which is a form of simplicity. :)
May
24
revised The limit is that which is neither too big nor too small to be the limit.
whoops, got a little dyslexic there!
May
24
answered The limit is that which is neither too big nor too small to be the limit.