Reputation
296,596
Next tag badge:
992/1000 score
280/200 answers
Badges
27 289 583
Newest
 Enlightened
Impact
~4.5m people reached

Oct
31
comment Given some ultrametric space $X$, is its completed metric $\hat{X}$ necessarily an ultrametric?
@Craig: I did indeed mean $m\in\Bbb N$; that was a typo. Fixed now; thanks!
Oct
31
answered Given some ultrametric space $X$, is its completed metric $\hat{X}$ necessarily an ultrametric?
Oct
31
comment Is symmetric difference (XOR) commutative?
@ronno: It isn’t a matter of considering them different things: they are different things. That there is a useful natural correponsdence between them does not change this fact, and you do the OP no favors by misleading him on this point. Students (as a group) have a hard enough time learning to use mathematical language precisely.
Oct
31
comment Is symmetric difference (XOR) commutative?
@ronno: What you’ve just said is that if you pretend that two different things are the same thing, then there is no difference between them. This simply isn’t so. Despite the obvious relationship between them, symmetric difference and exclusive or are not the same thing.
Oct
31
comment Is symmetric difference (XOR) commutative?
@Bob: $A\mathbin{\triangle}B=(A\setminus B)\cup(B\setminus A)$, and $B\mathbin{\triangle}A=(B\setminus A)\cup(A\setminus B)$; these are clearly equal.
Oct
31
comment Ultrametric on a normed space (real or complex)
@Danielle: It’s a general theorem: if $f:X\to Y$ is continuous, and $C$ is a connected subset of $X$, then $f[C]$ is a connected subset of $Y$. (In the special case in which $X$ and $Y$ are $\Bbb R$ this is basically just the intermediate value theorem.) You’re welcome!
Oct
31
revised Is symmetric difference (XOR) commutative?
Spelling of 'commutative'.; edited tags
Oct
31
answered Ultrametric on a normed space (real or complex)
Oct
30
answered How many ways can the men not sit together and the women not sit together?
Oct
30
comment How many ways can the men not sit together and the women not sit together?
Do you mean that no two men are together and no two women are together?
Oct
30
comment Totally bounded metric space
@Pedro: I win: $8>6$, so $h$ beats $f$. :-)
Oct
30
comment Totally bounded metric space
@George: You’re very welcome.
Oct
30
answered Totally bounded metric space
Oct
30
answered Bounded and open, cover
Oct
30
comment Compact set and finite definition
@sayuri: That’s correct: the open cover $$\left\{\left(0,1-\frac1n\right):n\ge 2\right\}$$ has no finite subcover, so $(0,1)$ is not compact.
Oct
30
comment Fibonacci Recursion Equation
@Kristen: Sounds like you did the right thing, and no, you shouldn’t need to prove that.
Oct
30
comment Fibonacci Recursion Equation
@Kristen: It is indeed. Now multiply out the rest to get $$a_{n+1}a_n-a_{n-1}a_{n+1}-a_{n-1}a_n\;,$$ combine the two terms that contain $a_n$, and see if you can then use the last comment in my answer.
Oct
30
comment What are all $n\in\mathbb{N}$ such that $\frac{n+13}{n-7}\in\mathbb{N}$?
Yes, that’s exactly right.
Oct
30
answered Compact set and finite definition
Oct
30
comment Fibonacci Recursion Equation
@Kristen: Okay, let’s start with the easiest bit: what’s $(-1)^n+(-1)^{n-1}$?