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Aug
25
comment How many ways can 6 cars ( 3 pink, 2 orange and 1 yellow) be parked in 6 parking slots in a row?
What is $_3P_2$?
Aug
25
comment Check dedekind cut for root 2
@user247327: "B is the set of all positive rational numbers whose square is larger than 2. (As Jorge said, you need "and" not "or" in your definition of B.)" Given that it is a problem statement, it is well possible that "or" is correct, and he is supposed to arrive at the conclusion that it is not a Dedekind cut.
Aug
25
comment As of August 2015, is the “set” of all gold medalists in the 2016 Olympics a set?
If using standard set theory (ZFC), the only items that can be element of a set are other sets. Assuming the 2016 Olympics gold medallists will not be sets (which I expect to be the case), they cannot be members of a ZFC set. If not using ZFC, it depends on the set theory you use.
Aug
25
comment Is f(x) = x smooth?
@zhw.: Is there any definition of "smooth" that does not apply to $f(x)=x$?
Aug
24
answered Intuition about an orthogonal projection operator for matrices
Aug
24
revised Intuition about an orthogonal projection operator for matrices
clarified the post (see comments)
Aug
24
comment Intuition about an orthogonal projection operator for matrices
Ah, now I understand: $\mathcal P_T$ is acting on $Z\in\mathbb R^{m\times n}$. I understood your text as $\mathcal P_T$ being parametrized by $Z$. I'll edit your post to make that more clear.
Aug
23
comment Intuition about an orthogonal projection operator for matrices
As far as I can see, $\mathcal P_T$ is an $m\times n$ matrix. How am I supposed to square that?
Aug
23
comment Which is greater, $98^{99} $ or $ 99^{98}$?
@MarkoKarbevski: I don't doubt that it holds. But the question was how to explain it at junior school level. And at junior school level you cannot assume that your audience can derive that.
Aug
23
comment Which is greater, $98^{99} $ or $ 99^{98}$?
You still need to justify the first greater-than sign.
Aug
23
comment how do you solve $(x^2-5x+5)^{x^2-36} =1$
How do you get four discrete solutions for the second displayed equation? I'm pretty sure that $z^2-5z+5 = \exp(\mathrm i\alpha)$ has a solution for every $\alpha\in [0,2\pi)$, and I'd be very surprised if those solutions would not depend continuously on $\alpha$.
Aug
23
comment how do you solve $(x^2-5x+5)^{x^2-36} =1$
What about $a=\mathrm e$ and $b=2\pi\mathrm i$?
Aug
23
comment Intuition about an orthogonal projection operator for matrices
Since $\mathcal P_T$ maps between two different spaces, it cannot be a projector, since the defining equation $P^2=P$ is not even defined for $P=\mathcal P_T$.
Aug
23
comment Intuition about an orthogonal projection operator for matrices
Ah, I see. But "projectors onto $U$ and $V$" doesn't make sense. Rather, they are the projectors onto the image and the orthogonal space of the kernel.
Aug
23
comment Intuition about an orthogonal projection operator for matrices
Since $U$ and $V$ in the real SVD are orthogonal, $UU^T$ and $VV^T$ are both the identity. While technically the identity is an orthogonal projector, I'm pretty sure it's not what you had in mind.
Aug
23
revised The value of limit $y^3/(x^3 – y^2 - 1)$ as$ (x,y) \rightarrow(1,0) $along the line$ y = x-1$?
fixed LaTeX in title
Aug
22
comment Find the limit (as x approaches 1) of : $|x^2+x-2|/(x^2-1)$
I notice that the output of the limit calculators is the average of left and right limit. Coincidence?
Aug
22
comment How to simplify $x^{1/2}$
I'm not sure I'd consider $1/x^3$ to be simpler than $x^{-3}$.
Aug
22
comment How do 24 significant bits give from 6 to 9 significant decimal digits?
Why are you assuming rounding down instead of rounding to nearest?
Aug
22
comment How do 24 significant bits give from 6 to 9 significant decimal digits?
@Kareem: How many different values can you represent with 23 bits?