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Jun
12
comment Why infinity multiplied by zero was considered zero here?!
While this explains the convergence, it doesn't really answer the OP's question, which was how the ratio test works in this case. The correct answer seems to be this one
Jan
8
comment Pedagogy: How to cure students of the “law of universal linearity”?
More to the point, you have to be able to deal with non-integer exponents.
Jan
8
comment Pedagogy: How to cure students of the “law of universal linearity”?
@JoshuaTaylor How is it different from $3(a+b) = a+b+a+b+a+b = a+a+a+b+b+b = 3a+3b$?
Oct
1
comment Does a red/blue coloring of the infinite subsets of $\mathbb{N}$ necessarily give an infinite monochromatic $M\subset \mathbb{N}$?
Interesting that your answer relies on the cardinality of $\mathbb N$, which the other answers don't. Your answer extends to sets up to size $\mathfrak c$, but not larger. I still like your answer, nevertheless.
Sep
12
awarded  Commentator
Sep
12
comment Is $\{\emptyset\}$ a subset of $\{\{\emptyset\}\}$?
What you are really noticing when you look at the form is that "the set $\{\{\emptyset\}\}$" contains the element $\{\emptyset\}$. $\{\emptyset\}$ is an element of $\{\{\emptyset\}\}$, not a subset of it.
Sep
2
comment Slice of pizza with no crust
In the mathematical formulation, you don't say anywhere that the subsets $A_i$ should be pairwise disjoint (or even almost pairwise disjoint). That would seem to be essential; otherwise the problem might be trivial.
Sep
2
comment Slice of pizza with no crust
I wonder how the mathematical formulation is "more concrete" than the physical description of the problem!
May
24
comment Topology of the power set
Current link is here. (I would have edited it into the answer but the system won't allow me to change just one character.)
May
6
revised Why is it important to study combinatorics?
fixed typo "Brauer" -> "Brouwer"
Mar
8
comment What was the first bit of mathematics that made you realize that math is beautiful? (For children's book)
There was a song about this on Square One TV years ago: "Nine Nine Nine" with the refrain "Nine nine nine, that crazy number nine. Times any number you can find, it all comes back to nine!"
Mar
5
comment What pattern does set theory study?
If mathematics is the science of patterns, does it follow that one branch of mathematics must study one particular pattern?
Mar
4
revised $f_n:D \rightarrow \mathbb{R}$ seq. of functions, $f_n$ continuous, $f_n$ conv. pointwise but not uniformly to $F$, $F$ be continuous?
added subscript n to function name (indicating sequence of functions)
Mar
4
suggested suggested edit on $f_n:D \rightarrow \mathbb{R}$ seq. of functions, $f_n$ continuous, $f_n$ conv. pointwise but not uniformly to $F$, $F$ be continuous?
Mar
4
awarded  Editor
Mar
4
revised When a prime number p divides $ab$ then we have either p divides a or p divides b.Prove that $\sqrt {p} $ is not rational for any prime number p.
fix square root sign, added math mode, fix spacing
Mar
4
suggested suggested edit on When a prime number p divides $ab$ then we have either p divides a or p divides b.Prove that $\sqrt {p} $ is not rational for any prime number p.
Feb
18
comment How do I understand $e^i$ which is so common?
The convention is to measure angles counter-clockwise, not clockwise. This should be a simple fix in two places. Also in one place you wrote $e^{ix}$ where you meant $y$ instead of $x$.
Feb
12
comment Does this prove that there are no infinite sets?
Aside from the various other problems with the argument, the conclusion "So there can be no infinite sets" should (at best) be weakened to "So the infinite set we posited at the beginning of this argument cannot exist."
Feb
1
awarded  Analytical