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May
1
comment almost sure convergence for non-measurable functions
You may as well ask what you can do with non-measurable random variables $X$. You can't integrate them, nor find a CDF, or even ask what the probability of say, $X=1$ is. Ultimately, you can make anything you want converge to something if you define it properly but the usefulness of it leaves something to be answered.
Apr
30
comment Does gradient descent and normal equation give the same answer?
You probably did something wrong. Check that you are updating your gradient descent correctly, especially the step size. For example, is your gradient descent even converging to something or is it bouncing between two values?
Apr
30
comment Is $\log(x_n+y_n)/\log(x_n)\to 1$?
Clearly if $x_n\rightarrow L$ for $1<L<\infty$, then the second limit is just $\log(L+1)/\log(L)$. If you want it to always be 1, then you need $x_n\rightarrow\infty$. If $x_n\rightarrow 1$, then the limit blows up.
Apr
30
comment Solving the inverse loop
Again, you are missing $\pm$ in your solution. And take a pair $(y,x)$ that satisfies $y=\pm\sqrt{r^2-x^2}$. It clearly also satisfies $x=\pm \sqrt{r^2-y^2}$ and vice versa. The solution set is the same. The graphs are exactly the same as well. As a simple example, $y=1/x$ has exactly the same graph as $x=1/y$, assuming you put $x$ on the $x$-axis and $y$ on the $y$-axis in both cases. If you don't then yes, the graphs are "different" but the solution set is exactly the same.
Apr
30
comment Sequence of independent events in a discrete probability space
When you say "discrete" space, does that also mean it's finite? Because the result is false if you consider the space of an infinite number of coin tosses, and let $A_i$ be the event that the $i$'th toss is heads.
Apr
30
comment Solving the inverse loop
Your question is confusing. Why would you expect a different solution for $y$? There's only one. The fact that $x,y$ have the same solution form is apparent from the fact that $x^2+y^2=r^2$ remains the same if you swap $x$ and $y$. You've also forgotten a $\pm$ sign in your solutions
Apr
30
comment Why did mathematicians introduce the concept of uniform continuity?
Compactness is definitely the key word here. For OP's benefit, here's a nice explanation: math.ucla.edu/~tao/preprints/compactness.pdf
Apr
30
comment Determine the Taylor Series for $(1+x)^n$ about $x=0$
@user2837598: the series has infinite number of terms if $n<0$.
Apr
29
answered Is there an algorithm for parametrization of equations?
Apr
29
comment Why it is necessary for copula functions to be grounded?
See this answer: math.stackexchange.com/questions/568669/2-increasing-functions I think in general you want the gradient to point into the positive quadrant of your space. So a $n$ dimensional increasing function would have gradient in the regiion $(+,+,+,\cdots,+)$.
Apr
29
answered Solving $a_n=5a(n/3)-6a(n/9)+2log_3n$ using domain transformation
Apr
29
comment Given $n$ points, can we always connect them such that every angle is at least $30°$?
You need to clarify what you mean by angle here. Is it the angle of common intersection of any pair of lines? For example, what if you put all the points in a straight line. What would be the angles between them? 0, 180?
Apr
29
comment Newtons Law of Cooling Differential Equations
Presumably the equilibrium corresponds to a stable fixed point of the system.
Apr
29
revised Sine and Cosine Expansion Problem
added 2 characters in body
Apr
29
comment Finding coefficients, Legendre polynomials.
Right, and by the looks of it you won't need legendre polynomials past $n=2$.
Apr
29
answered Sine and Cosine Expansion Problem
Apr
29
answered Finding coefficients, Legendre polynomials.
Apr
29
answered Why it is necessary for copula functions to be grounded?
Apr
27
accepted Sum-of-divisors determinant
Apr
27
comment Sum-of-divisors determinant
beautiful! Thanks!!