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visits member for 1 year, 11 months
seen Jun 12 '13 at 4:20

Nov
22
awarded  Yearling
May
27
comment $\mathbb{Z}:= \mathbb{N} \cup (-\mathbb{N}) \cup \{0\}$, $a,b \in \mathbb{Z}$, when $a \le b$?
What is the question?
May
22
answered Are all integer fractions rational?
May
22
comment Are all integer fractions rational?
I don't see why. But fine, how about $.499999...$?
May
22
comment Are all integer fractions rational?
$1/2 = .500000000000...?$
May
8
comment Looking for a differentiable function which behaves somewhat like $\min(x,1)$
This doesn't work for n odd.
Apr
19
comment Prove a square is homeomorphic to a circle
You're correct, he did decide to use the interior. You do not have to establish an inverse directly in order to show that a function is a bijection. Moreover, I think what was meant is (as I said) that you don't have to find the inverse and prove that it's continuous. It follows from the above (or would if we were dealing with the closures of the spaces)
Apr
19
comment Prove a square is homeomorphic to a circle
Cameron: it is a standard result that a continuous bijection from a compact space to a Hausdorff space is a homeomorphism. Both sets in the OP are closed, compact, and Hausdorff. So a continuous bijection implies a homeomorphism without having to find an inverse and prove it's continuous.
Apr
12
comment Measurable Functions - Constructing Examples
The pointwise limit of a sequence of measurable functions is measurable. So your second one (if I'm reading it correctly) is impossible.
Apr
8
awarded  Promoter
Apr
7
revised Measurability of a certain set in Falcolner's Geometry of Fractal Sets
added 304 characters in body
Apr
6
asked Measurability of a certain set in Falcolner's Geometry of Fractal Sets
Mar
23
comment Countably monotone does not imply monotone and countably additive?
You're looking for a set function which is countably subadditive but not countably additive? Try Lebesgue outer measure on the powerset of $\mathbb{R}$. It's countably subadditive but is not countably additive (in general).
Mar
16
answered Proof by contradiction - help!?
Mar
16
comment Pushforward measure integral property
What have you done so far? Try starting when $f$ is simple.
Mar
13
comment If x is rational, $x\ne 0$, and $y$ irrational, prove $x+y, x-y, xy, x/y$ and $y/x$ are all irrational.
You need to show that $x +y$ is irrational if $x \neq 0$ is rational and $y$ is irrational; we assume $y$ is irrational. If it were the case that $x + y$ is a rational number, then $(x+y) - x$ would also be a rational number. But that's just $y$, which contradicts our assumption that $y$ is irrational.
Mar
12
comment If every compact set is closed, then is the space Hausdorff?
The title and question are different. The title asks if every compact set is also a closed set, is the space Hausdorff. The question asks if every set is closed and compact, is it Hausdorff. Which do you mean?
Mar
10
comment Existence of the limit from the left of real distribution functions
It follows from the fact that $f$ is nondecreasing.
Mar
10
comment How can I define a function to show that $\{3^n\mid n\in\mathbb{Z}\}$ is countably infinite?
Do you know that $\mathbb{Z}$ is countably infinite? If so it's straightforward. Let $f$ be a bijection from $\mathbb{N}$ to $\mathbb{Z}$. Then map each $n \in \mathbb{Z}$ onto $3^n$. Now compose.
Mar
8
revised $\mathbb{R}^S$ for finite and countable set $S$
added 144 characters in body