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Aug
14
comment Complex Analysis Limits
They don't get $1+i$ from $\lim_{x\to 0} \frac{f(x+ix)-f(0)}{x+ix}$. If the function were differentiable, they would get that result. They don't, so the function is not differentiable.
Aug
12
awarded  Guru
Aug
11
awarded  Good Answer
Aug
11
comment How many values does $i^{i^z}$ have?
$i = e^{i\frac{\pi}{2}+2\pi k}$. Now use rules of exponentiation.
Aug
11
comment How many values does $i^{i^z}$ have?
It means $i$ raised to the power $z$. It's like $2^x$, except with complex numbers.
Aug
11
comment How many values does $i^{i^z}$ have?
Consider first functions of the form $f(z)$ that could send $i^{f(z)}$ to only finitely many values. For instance, what if $f(z)$ was such that $f : \mathbb{C} \to \mathbb{Z}$?
Aug
11
comment What's the opposite of damping?
I disagree. In the typical spring-mass-damper, $m\ddot{x} + c\dot{x}+kx = F(x,t)$, the "forcing" term is $F(x,t)$, but the damping coefficient term is $c$. Changing signs on $c$ such that the damping effect is reversed is not the same as adding a forcing function.
Aug
11
comment Logic behind dividing negative numbers
Alternatively: if you have accrued \$100 in debt with purchases of \$20 each, you have made $\frac{-\$100}{-\$20} = 5$ payments.
Aug
11
awarded  Enlightened
Aug
11
awarded  Nice Answer
Aug
11
answered Logic behind dividing negative numbers
Aug
11
awarded  Peer Pressure
Aug
10
comment An integral that might contain a typo
The factor of 299 here is extremely interesting...
Aug
7
answered 3 points on “horizontal” sinusoid, what is its period?
Aug
5
comment Find the general solution to
Oh, and Kaster beat me to it in a comment :/
Aug
5
answered Find the general solution to
Aug
4
answered Exponential distribution - Using rate parameter $\lambda$ vs $\frac{1}{\lambda}$
Aug
3
comment Find the sum of the digits in the number 100!
@bibstha Arguably, the prime factorization reduces the total number of Cauchy products. Probably. For $n \le 100$, any term in the product $n!$ has at most one power of a two-digit prime as a factor. So the prime factorization of the products allows us to gather things up and compute very easily some powers of primes. Then we can convolve a rather small number of numbers, which might be more efficient.
Aug
3
comment how to differentiate an indicator function?
The sum of an indicator function looks like a staircase. A smooth approximation to a staircase looks like a handicap ramp. More or less...
Aug
1
comment Studying mathematics: Is proving things yourself worth the time?
Can you learn to speak a language without practicing speaking? Can you learn to play guitar simply by reading sheet music?