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I have an account here mostly so that I can ask stupid questions. Hopefully over time my questions will become less stupid, or at least more complicated and therefore laughably naive only to a select few experts.

I am an undergraduate. Most or all of my questions here are from self-study, so I really appreciate the answers given.


Jul
9
awarded  Nice Answer
Jul
5
accepted Complex measures vs. Positive Measures
Jul
5
comment Complex measures vs. Positive Measures
That makes sense, thanks.
Jul
5
comment Complex measures vs. Positive Measures
I guess I'd be curiuous to know why he does so, but presumably I'll find out when I read that chapter. I didn't realize that a "complex function" precluded taking values at $\infty$, unlike a positive function.
Jul
5
asked Complex measures vs. Positive Measures
Jul
3
comment Ordered rings $R$ with $ab = ba$, $ab \leq ba$ or $ba \leq ab$ for all $a, b \in R$?
Sorry - I meant what I put in the title. Although now that I think about it again I guess its the same thing as Qiaochu suggests.
Jul
3
revised Ordered rings $R$ with $ab = ba$, $ab \leq ba$ or $ba \leq ab$ for all $a, b \in R$?
edited body
Jul
3
asked Ordered rings $R$ with $ab = ba$, $ab \leq ba$ or $ba \leq ab$ for all $a, b \in R$?
Jul
2
awarded  Curious
Jul
2
awarded  Inquisitive
Jun
28
accepted “Geometric” proof of Rouche's theorem on the number of zeros?
Jun
26
answered How were 'old-school' mathematics graphics created?
Jun
25
comment How can I make this proof more precise / detect the small error
@steffens21 I confess that I thought $I = [0,1]$ in this question.
Jun
25
comment Why do fields seem to be a prerequisite for calculus?
@Anthony For integration - you need to multiply the measure of each interval in the partition by the estimated height at that point, since we are trying to estimate the area under the curve. Since multiplication is the basic operation for finding area, I would think that it could not be avoided unless you are willing to work in a discrete setting where multiplication is just repeated addition. That's just my guess though.
Jun
25
comment Why do fields seem to be a prerequisite for calculus?
I suppose one reason is that the definition of a derivative uses both addition and division.
Jun
25
comment Expressing $\Bbb N$ as an infinite union of disjoint infinite subsets.
I like this because it avoids everything but the essential set theoretic structure...
Jun
25
comment How can I make this proof more precise / detect the small error
@steffens21 A compact set is closed in a Hausdorff space, so it's preimage is closed. Since the domain is compact, it follows that the preimage is compact. (A closed subset F of a compact subset K is compact - any open covering of F can be extended to an open covering of K by adding $K \setminus F$. Then, remove $K \setminus F$ from the finite subcovering of $K$.)
Jun
24
comment How can I make this proof more precise / detect the small error
Is something unclear?
Jun
22
accepted Stability of the nonempty intersection of an open set $A$ with a set $S$ under homotopy?
Jun
22
comment Stability of the nonempty intersection of an open set $A$ with a set $S$ under homotopy?
Lovely - I was struggling to express a similar idea, so I think I have learned something from this. Do you have any idea why it fails in the case of open maps?