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Squirtle, squirtle......


Jul
17
answered Show that for any subsets $A,B\subset X$: (i):$d(A\bigcup B)\leq d(A)+d(B)+d(A,B)$ and (ii) $d(\bar A)=d(A)$
Jul
16
comment How find the value of the $x+y$
By $R$ you mean $\mathbb{R}$?
Jul
15
comment Are there formal systems that are not logical systems?
Would such a formal system be illogical?
Jul
15
comment Is this Goldbach-type problem easy to solve?
Well.... I'll change my vote back... Just seems like (1): You answered before you understood what was going on, (2) You have a ton of rep, so you should probably chill.
Jul
15
comment Can the value of $(-9!)$ be found
I made a really bad typo on my phone and wasn't able to edit it there...... I wanted to say, "You can define something however you wish; then people can do whatever they want with it."
Jul
11
comment If $f$ has pole of order $m$, then $\text{res}\left(f,z_0\right)=\lim_{z\to z_0}\frac{1}{(m-1)!}\left\{(z-z_0)^mf(z)\right\}^{(m-1)}$
Its only zero if there are no poles, or more precisely: $\int_\gamma f(z)dz=0$ whenever there is no pole.
Jul
11
answered To show closedness of a subset in a metric spaces
Jul
10
comment writing a simple matrix
This really belongs on stack overflow.
Jul
10
comment Showing that $f:\mathbb{Z}_4\rightarrow \mathbb{Z}_2$ given by $f(x)=[3x]$ is function?
The statement "showing that $3x-3y=2k$ for an integer $k$" is precisely equivalent to the stuff I wrote after $[0]$
Jul
10
comment Showing that $f:\mathbb{Z}_4\rightarrow \mathbb{Z}_2$ given by $f(x)=[3x]$ is function?
The three is arbitrary as far as I'm concerned (there's no need for this function to be defined the way it is; it just is). In our case zero mod four goes to zero mod two because $f(0)=[3(0)]=[0]$.
Jul
10
answered Showing that $f:\mathbb{Z}_4\rightarrow \mathbb{Z}_2$ given by $f(x)=[3x]$ is function?
Jul
10
comment How does one graph $\sum_{x=0}^{n}$
If you change it to $f(n)=\sum_{i=0}^n i$ then the ordinary step function $S$ is the CDF of $f$. This isn't what you have, but very close so you can think of it in terms of CDFs, if that helps.
Jul
8
comment Determine if the following functions are multiplicative…
I've just realised that my proof shows it's not TOTALLY multiplicative, so in summary: the first is multiplicative but not totally, the second example isn't even multiplicative (for coprimes)
Jul
8
comment Determine if the following functions are multiplicative…
Yes, as Andre pointed out, for some k, this is multiplicative. We can assign a different function for each fixed k, like $f_k(n)=(n,k)$, then think how we use relative primes as he suggests.
Jul
8
revised Determine if the following functions are multiplicative…
added 32 characters in body
Jul
8
comment Determine if the following functions are multiplicative…
Apologies for the silly mistake I made earlier, hopefully I didn't confuse you ; I've fixed it, it should be clear now.
Jul
8
revised Determine if the following functions are multiplicative…
deleted 1 character in body
Jul
7
comment Determine if the following functions are multiplicative…
en.wikipedia.org/wiki/Multiplicative_function
Jul
7
answered Determine if the following functions are multiplicative…
Jul
7
comment Proof Verification: $ (ab)^{-1}=a^{-1}b^{-1}$
I'm not sure I follow you... What do you mean, "Is that enough to assume the "/"?"?