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Aug
13
comment the real sequence $\{p_n\}$ is defined as $p_1=2, p_{n+1}=( 2+p_n)/(2p_{n}+1)$
It bothers me that they didn't start at $p_1=0$, giving $p_2=\frac{2+0}{2·0+1}=2$.
Aug
4
comment Goldbach Conjecture predicate form?
The Goldbach Conjecture speaks about "every even integer $n$". Your claim only concerns an infinite number of such $n$'s. I don't know an argument right of my head of why that's true, though.
Aug
2
revised $\lim_{x\to 0^-} \frac{\pi x\log(x) + \pi x^2}{(x^2-1)^2}$ should not be defined, right?
added 176 characters in body
Aug
2
answered $\lim_{x\to 0^-} \frac{\pi x\log(x) + \pi x^2}{(x^2-1)^2}$ should not be defined, right?
Jul
30
awarded  Nice Answer
Jul
30
awarded  Explainer
Jul
30
revised How to divide by a matrix
deleted 1 character in body
Jul
30
answered How to divide by a matrix
Jul
29
comment Solve for $x$ - Logarithm Equation $\ln x+\ln(x+1)=\ln 2$
@YvesDaoust: Yes, I guess one should drop the "real part" to see the complex one too (here). I don't know OPs background and left it to him to argue $x>0$. The wolframalpha page explicitly tells you the root too, though.
Jul
29
comment Are the quantifiers interchangeable?
Reference
Jul
29
comment Solve for $x$ - Logarithm Equation $\ln x+\ln(x+1)=\ln 2$
Just to check, you could just look at the graph on the web.
Jul
29
answered Do “small” and “large” numbers actually exist in an absolute sense?
Jul
28
awarded  Good Question
Jul
24
comment Point of intersection of $f_a(x)=ax^{2}+3x+1$ and $g_b(x)=\frac{b}{x}$
Yes. Expressing a condition $f(x)=\frac{b}{h(x)}$ in therms of $b$ gives $b=h(x)\,f(x)$, where we've not even considered $x=1$ in particular. For your functions this equation says $b=x\,(ax^2+3x+1)$, which is a relation between $b, a$ and $x$. You're interested in the point $x=1$, leaving you with $b=a+4$, a relation between $b$ and $a$.
Jul
21
awarded  Nice Question
Jul
16
comment What good is infinity?
I guess I like your answer, but I don't support to state opinions as if they were fact. In particular, the claim "[The reason is that] philosophical arguments aren't a very good method for making decisions."
Jul
16
comment $\lim_{n\rightarrow\infty}\frac{1}{n}\sum_{k=1}^{n}\frac{k}{k^{2}+1}$
Where does the $\int_0^1$ come from? Are you saying this $L$ is the same value of the sum in OPs question?
Jul
14
awarded  Nice Question
Jul
10
revised Integrate $\ln x \cos(\ln x) \,dx$
deleted 17 characters in body
Jul
10
accepted How is the extended real number line modeled?