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Jul
3
answered Trouble Understanding Notation in Reinforcement Learning Paper
Jun
28
comment Integral with only a list of values
I was a bit vague about the meaning of "under" because: suppose $a<b<c<d$ and suppose $f(a<x\leq b),f(c\leq x<d)\geq 0$ and $f(b\leq x\leq c)<0$. Then the the integral on $[a,d]$ does not define the area "under" (i.e. between the function and the x-axis), since the contribution of the integral on $[b,c]$ will be negative. Area is by definition always positive, so we need to be careful. Also, consider $\int_0^1 x^{−1/2}$. We have $\lim_{x→0}x^{−1/2}=\infty$, but the area under the curve is perfectly finite.
Jun
27
answered Integral with only a list of values
Jun
26
comment Solving $2^x - 3^x + 6^x =0$.
Thanks for your answer. I will take a look later when i get a spare bit of time.
Jun
26
comment Solving $2^x - 3^x + 6^x =0$.
@Did you originally stated $-x $ in the exponents... maybe that's it? On the move so can't check...
Jun
26
asked Solving $2^x - 3^x + 6^x =0$.
Jun
25
comment Find all complex numbers so that $Im(\frac{z+2}{2-i})=1$ and $Re(z^2+1)=1$ and for $z$ which is in the first quadrant find $\sqrt{z}$
I think you made a mistake in your 5th line down (see @mathlove's answer)
Jun
25
comment Looking for a bound on a function involving $\sinh$
Having played around with the function's Taylor expansion I think I can say that $\text{sech}(ct)$ is an upper bound... not proved it though... not sure if this helps with your question any either !
Jun
24
comment Need Suggestions for beginner who is in transition period from computational calculus to rigorous proofy Analysis
I'd recommend reading How to Think Like a Mathematician by Kevin Houston first. I wish I had done!
Jun
24
revised Derivative of the Riemann zeta function for $Re(s)>0$.
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Jun
24
comment Riemann Zeta Function and Including Complex Numbers
See also this question which shows an analytic continuation of the Riemann zeta function to $\Re (s)>0$... math.stackexchange.com/questions/256992/…... an improvement on $\Re(s)>1$, but still not the whole story !
Jun
24
comment My brother asked me to explain a algebra problem. How should I explain it?
You're very welcome ! Welcome to SE.
Jun
24
answered My brother asked me to explain a algebra problem. How should I explain it?
Jun
21
comment Why $\sum\limits_{n=1}^\infty \frac{e^{inx}}{n}=-ln(1-e^{ix})$ in $D'$
Not quite sure about the question, but maybe this will help: Your sum is just $\sum_{n=1}^\infty\frac{(e^{ix})^n}{n}$, and $\sum_{n=1}^\infty \frac{z^n}{n}$ is a well known power series...
Jun
17
revised On norms for “more complicated objects”
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Jun
11
revised Can every definite integral be expressed as a combination of elementary functions?
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Jun
10
awarded  Nice Answer
Jun
10
revised Express 99 2/3% as a fraction? No calculator
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Jun
9
answered Express 99 2/3% as a fraction? No calculator
Jun
9
comment Why is $e$ so special?
Thinking aloud: the function $e^x$ has many interesting properties, e.g. if we consider the function $e^x$, then we find the derivate of $e^x$ is itself $e^x$. This is quite remarkable ! When $x=1$ we obtain $e^1=e$. $e^x$ is also strictly positive for all $x\in\mathbb{R}$. $e^x$ is also a transcendental function. Another remarkable formula involving $e^x$ is $e^{i\pi}+1=0$, where $i=\sqrt{-1}$.