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bio website linkedin.com/in/gt6989b
location New York, NY
age 35
visits member for 3 years, 1 month
seen Oct 20 at 1:37

Aug
31
comment 2 examples to try to understand partials derivatives and deriviability
A discontinuous function is not differentiable. In any number of dimensions. You can design a continuous variant that would be differentiable, but that would not be the function itself.
Aug
28
comment Omega Notation and Average Running Time Problem
@MounaMokhiab think about how you compute average-case running time for an algorithm. you compute what it's performance is on a set of all possible inputs and take the average. when you take the average, it may do bad on a very small section of inputs but do ok on the rest - since you are averaging over a very large quantity - it will take out any factor of your choice. Randomization was just a simplest way to give an example of this.
Aug
28
comment There is no nonconstant entire function $f$ such that $f(z+1)=f(z)$ and $f(z+i)=f(z)$
Makes sense to me
Aug
28
comment Omega Notation and Average Running Time Problem
@MounaMokhiab yes, same method as Snufsan described in the above comment: toss $f(n)$ coins if all heads, waste $n^n$ time and do something in $n^2$, else do something in $n^2$. Total running time is $2^{-f(n)} n^n + (1-2^{-f(n)}) n^2$ and now if $f(n)$ is large enough you are good to go.
Aug
28
comment Is$\frac{\sqrt{a}}{\sqrt{b}}$ the same as $\sqrt{\frac{a}{b}}$?
Yes, they are different, but where both are defined (i.e. on the intersection of domains) - the values will coincide.
May
14
comment Find the distribution of $X_1^2 + X_2^2$?
@user111548 Yes.
May
14
comment Find the distribution of $X_1^2 + X_2^2$?
@user111548 no. I meant that the mgf of $X$ and mgf of $X/\sigma$ are not the same thing.
May
5
comment Proving breath first traversal on graphs
@DrJonesYu Think about what $\textrm{Next}$ is at iteration $k$ -- this is a set of all vertices $x \in V$, such that for some $u \in V$, which is $k-1$ steps from $r$, there is an edge $(u,x)$. But that means $x$ is in the connected component of $r$.
May
5
comment Conditional CDF
@Someone i think so, made the edit
May
5
comment How prove this $ n = \frac {a^3 + 2b^3} {c^3 + 2d^3}. $ infinitely many special numbers
For (2), from your equation follows that $a^3$ is even, so $a$ is even, so $a = 2A$ and the equation becomes $$4A^3 + b^3 = 19 \cdot 53 (c^3 + 2d^3),$$ and $b$ and $c$ must have the same parity.
May
5
comment Evaluate $\frac{2}{4}\frac{2+\sqrt{2}}{4}\frac{2+\sqrt{2+\sqrt{2}}}{4}\cdots$
Moreover, it's easy to see it is an increasing sequence, you just need to show it is bounded above.
May
5
comment Evaluate $\frac{2}{4}\frac{2+\sqrt{2}}{4}\frac{2+\sqrt{2+\sqrt{2}}}{4}\cdots$
The only thing i can think about - prove that the sequence of terms is a Cauchy sequence. This only requires differences between successive terms.
May
5
comment Evaluate $\frac{2}{4}\frac{2+\sqrt{2}}{4}\frac{2+\sqrt{2+\sqrt{2}}}{4}\cdots$
Numerically, converges to about $0.405284735 \approx \ln(1.5)$
May
1
comment Geometric and algebraic definitions of the dot product , proof of equivalence?
nice and elegant
May
1
comment Geometric and algebraic definitions of the dot product , proof of equivalence?
They do, you just have to express $\cos \theta$ in terms of $a_x, a_y, b_x, b_y$ and do the arithmetic.
May
1
comment How to find the full Taylor expansion of the following:
@user88595 fixed...
May
1
comment Geometric and algebraic definitions of the dot product , proof of equivalence?
Well, you claimed it's a proof -- before we show that, it's not really a proof, is it?
May
1
comment Geometric and algebraic definitions of the dot product , proof of equivalence?
Well, if $\vec{a} = a_x \hat{i} + a_y \hat{j}$, by definition, $$\left| \vec{a} \right| = \vec{a} \cdot \vec{a} = a_x^2 + a_y^2.$$
May
1
comment How to find the full Taylor expansion of the following:
@Frumpy partial fractions should reduce denominator to degree 1
May
1
comment Geometric and algebraic definitions of the dot product , proof of equivalence?
I don't understand why this is a proof of geometric and algebraic equivalence. Algebraically, you argued $$\vec{a} \cdot \vec{b} = a_x b_x + a_y b_y.$$ Geometrically, you argued that $$\vec{a} \cdot \vec{b} = \left| \vec{a} \right| \cdot \left| \vec{b} \right| \cos \theta = \sqrt{a_x^2 + a_y^2} \sqrt{b_x^2 + b_y^2} \cos \theta. $$ Why are they the same???