190 reputation
6
bio website endlesstweet.blogspot.hk
location Hong Kong
age
visits member for 2 years, 8 months
seen yesterday

I'm Chinese. I am learning English, so I am maintaining a blog written in English. Welcome to my blog and leave your comments! Thanks :p


Apr
15
comment How can I learn Real Analysis in 10 days?
I think the procedure would be quite like "Teach yourself C++ in 21 days".
Apr
11
answered Prove that $f(x)=(e^x-1)(x^2+3x-2)+x$ has exactly one positive root, exactly one negative root and one root at $x=0$.
Apr
10
comment Prove that $f(x)=(e^x-1)(x^2+3x-2)+x$ has exactly one positive root, exactly one negative root and one root at $x=0$.
Solve $f'(x)=e^x (x^2+5x+1) - 2x -2 = 0$, i.e. $e^x (x^2+5x+1) = 2x +2$. Because $e^x$ doesn't change the sign of $x^2+5x+1$, $y=e^x (x^2+5x+1)$ at most has two intersection points with the line $y=2x +2$. Thus $f(x)=0$ at most has three roots, and you have found them all.
Apr
10
comment Power calculation for simplification?
@RoyiNamir Not quite. But for further information about that, I suggest you read wikipedia pages about IEEE754, "float", and "double". If you have any problem on these issues, it may be better to ask it on stackoverflow.com
Apr
10
comment Power calculation for simplification?
@RoyiNamir 6.805647*10^38 - 0.000000406*10^38 = (6.805647-0.000000406) * 10^38. Please distinguish "multiplication" and "power" :)
Apr
10
comment Power calculation for simplification?
@RoyiNamir of course not. I just separately calculate X^y and Z^y, and then do the subtraction.
Apr
10
comment Power calculation for simplification?
@RoyiNamir sorry, I don't quite catch you. In this answer I mean we can separately calculate 2^129(=6.805647*10^38) and 2^105(=4.06*10^31=0.000000406*10^38), and then do the minus: (6.805647-0.000000406)*10^38. Is there any problem?
Apr
9
revised Power calculation for simplification?
added 70 characters in body
Apr
9
answered Power calculation for simplification?
Apr
9
awarded  Commentator
Apr
9
comment Power calculation for simplification?
Don't forget "log".
Apr
9
answered why is frobenius norm of a matrix greater than or equal to the 2 norm?
Jun
8
awarded  Autobiographer
Jun
6
comment How can I explain $0.999\ldots=1$?
It's a circular argument.
Jun
6
awarded  Critic
May
25
answered What do we call the angular arcs between two edges of triangles?
May
25
comment Infinite series and its upper and lower limit.
@hyg17: you may see the original definition of convergence for a real series. The problem of your question is the ambiguous expression, as you have noticed, your "first" $a_n$ is not the same as your "However" $a_n$. BTW, if you comment on others' comment, please use @somebody to let him know :)
May
25
comment Infinite series and its upper and lower limit.
It reminds me the series: $1+1-1+1-1+\cdots$. You can consider it as $1+(1-1)+(1-1)+\cdots=1$ or $(1+1)-(1-1)-(1-1)-\cdots=2$. So, as it's unclear specified and can be converged to different values, the series actually diverges.
May
25
awarded  Editor
May
25
revised Is $\sum\limits_{k=1}^{n-1}\binom{n}{k}x^{n-k}y^k$ always even?
added 56 characters in body