Reputation
1,381
Top tag
Next privilege 2,000 Rep.
Edit questions and answers
Badges
1 6 19
Impact
~16k people reached

1d
revised Why is this class closed under difference?
added 83 characters in body
1d
revised Why is this class closed under difference?
added 83 characters in body
1d
comment Why is this class closed under difference?
You're correct. I abused notation too bad. I'm updating it
1d
revised Why is this class closed under difference?
added 11 characters in body
1d
asked Why is this class closed under difference?
May
16
comment Why, intuitively, is the order reversed when taking the transpose of the product?
This is the most trite answer i have ever seen. I can't decide whether it deserves an upvote or a downvote.
Apr
28
awarded  Autobiographer
Apr
25
comment Borel $\sigma$-algebra defintion question
You may want to read the first few pages of Lee's Topological Manifolds, which gives a nice, light but precise idea of what we mean when we call a set `open.'
Apr
24
comment Borel $\sigma$-algebra defintion question
Sigma algebras are supposed to tell you 'what you're able to measure. So a sigma algebra thats ``larger'' than other sigma-algebras is one that can measure more stuff. It's just a superset of other sigma algebras. For instance, the set $\{a,b,c\}$ admits these sigma algebras: $$\{\{\},\{a,b,c\},\{a\},\{b,c\}\}$$ and just the power set: $$\{\{\},\{a,b,c\}, \{a,b\}, \{b,c\}, \{a,c\}, \{a\}, \{b\}, \{c\}\}.$$ You can easily verify they're both sigma algebras, but the powerset is larger than the other.
Apr
16
comment Understanding the definition of nowhere dense sets in Abbott's Understanding Analysis
For arbitrary $S$ and $B$, it may happen that all the Bosnians make fences separating themselves from the Serbs (no matter what size or shape, open or closed, just as long as there are no Serbs). More Bosnians come and stand on top of the fence. Whereas Bosnians previously only roamed inside the fences, now there are also Bosnians directly along all the borders too. (Closure) $$$$ Now if none of the Bosnians find themselves in an open region of only Bosnians, then $B$ is nowhere dense in $S$. In this case the Serbs have contained the Bosnians to isolated points.
Apr
16
comment Understanding the definition of nowhere dense sets in Abbott's Understanding Analysis
Not sure if this helps. $S$ is the Serbs and $B$ is the Bosnians. $B$ is nowhere dense in $S$ if we can take any Bosnian (who isn't also a serb; the analogy breaks a bit here), and put an open fence around him, so that throughout the inside the fence there are only Bosnians. $$$$ On the other hand if there was a place that $B$ was dense in $S$, then there would be some Bosnian who can't fence himself off from Serbs in an open way. That Bosnian would be topologically 'inseperable' in some sense from the Serbs. $$$$ Of course, precisely what `open' means depends on the topology you have.
Apr
14
revised $\arg\max$ of an increasing function grows as the region grows.
deleted 57 characters in body
Apr
14
comment $\arg\max$ of an increasing function grows as the region grows.
Apologies @MichaelGrant, I misrepresented my functions $f_i$. The $f_i$ don't have inflection points.
Apr
14
revised $\arg\max$ of an increasing function grows as the region grows.
added 67 characters in body
Apr
14
revised $\arg\max$ of an increasing function grows as the region grows.
added 32 characters in body; edited tags
Apr
14
revised $\arg\max$ of an increasing function grows as the region grows.
added 26 characters in body
Apr
14
asked $\arg\max$ of an increasing function grows as the region grows.
Apr
13
comment How is this definite integral solved: $\int_{-\sqrt3}^{\sqrt3}{e^x\over(e^x+1)(x^2+1)}dx $?
What have you tried>?
Feb
13
comment Finding a special determinant, $\det(I+SD)$
Whoops you're right! I was trying to pull $D$ out instead of grouping it with $h$. Thanks
Feb
13
comment Finding a special determinant, $\det(I+SD)$
Those results are impressive, but $D$ might not be invertible.