8,329 reputation
11639
bio website
location
age 43
visits member for 2 years, 1 month
seen yesterday

Apr
16
comment Subsets of $[0,1]$
OK, I interpreted it as subset of the $[0,1]$ interval in $\mathbb R$ (with the topology of $\mathbb R$). Anyway, when intersecting with the open interval, it's true for both.
Apr
16
comment Subsets of $[0,1]$
Note that you have to intersect with $(0,1)$, not $[0,1]$ because an open set was requested.
Apr
16
comment Subsets of $[0,1]$
It will not have the measure $\epsilon$ due to overlapping intervals (think of the rationals which lie inside the very first interval, for example). It will, however, have measure $\mu$ with $0<\mu<\epsilon$. In addition, you have to intersect with $(0,1)$ because otherwise it may not be a subset of $[0,1]$.
Apr
14
comment Probability of at least two events occurring.
If the question was asked at a meeting of the yellow party, the probability is negligible. ;-)
Apr
14
answered A question in combinatorics
Apr
13
revised If a nonempty set of real numbers is open and closed, is it $\mathbb{R}$? Why/Why not?
Added a short initial description about what the proof does
Apr
13
answered If a nonempty set of real numbers is open and closed, is it $\mathbb{R}$? Why/Why not?
Apr
13
comment If a nonempty set of real numbers is open and closed, is it $\mathbb{R}$? Why/Why not?
Well, showing that is showing that $\mathbb R$ is connected.
Apr
13
comment If a nonempty set of real numbers is open and closed, is it $\mathbb{R}$? Why/Why not?
With empty border. You prove the original statement by proving that.
Apr
13
comment If a nonempty set of real numbers is open and closed, is it $\mathbb{R}$? Why/Why not?
More exactly, its border is the empty set (the border as set of all border points is always defined, but the clopen set has no border points, and thus the border is empty).
Apr
13
comment If a nonempty set of real numbers is open and closed, is it $\mathbb{R}$? Why/Why not?
The border obviously cannot contain elements outside of $\mathbb R$ because we are talking about the topology of $\mathbb R$.
Apr
13
comment If a nonempty set of real numbers is open and closed, is it $\mathbb{R}$? Why/Why not?
A closed set contains all of its border. An open set contains none of its border. What do you conclude about the border of a set that is both open and closed?
Apr
13
comment Finding the largest factor of a number, possible without exhaustion?
Indeed, whoever finds an efficient algorithm will get famous. Unless an intelligence agency decides it's better to prevent him from publishing it ...
Apr
13
revised Proof that $\det(A)=\det(A^T)$ using permutations.
edited title
Apr
13
comment Finding numbers $a$ and $b$ for a complex number
BTW, with $a=1/2$ and $b=0$ the last equation would read $1-i=1$, which would mean $i=0$. Which quite obviously is not true.
Apr
13
comment Finding numbers $a$ and $b$ for a complex number
Hint: What are the real and imaginary parts of the number $1$?
Apr
13
comment Proof that $\det(A)=\det(A^T)$ using permutations.
You forgot to mention another necessary fact: $\operatorname{sgn}(\pi)=\operatorname{sgn}(\pi^{-1})$ — otherwise the two expressions would not be equal.
Apr
13
revised Multiplying Adjacent Matrices?
added 2 characters in body
Apr
13
revised Multiplying Adjacent Matrices?
mathematics formatting
Apr
13
answered Multiplying Adjacent Matrices?