Reputation
8,293
Top tag
Next privilege 10,000 Rep.
Access moderator tools
Badges
8 25
Impact
~118k people reached

Dec
2
comment In a limit proof, what are the assumptions?
@Amad27 Generally, to prove such things, you fix some arbitrary $\epsilon > 0$ and find the value of $\delta_2$, such that for any $x \in (a-\delta_2,a+\delta_2)$ you will have the desired inequality $||f(x)|-|L|| < \epsilon$.
Dec
2
revised How do I find the limits of integration?
added 54 characters in body
Dec
2
answered In a limit proof, what are the assumptions?
Dec
2
comment Calculation of all positive integer $x$ for which $\displaystyle \lfloor \log_{2}(x) \rfloor = \lfloor \log_{3}(x) \rfloor \;,$
you likely want $\ln x$ in the last inequality?
Dec
2
comment Innovation behind formula for surface area and volume of a sphere
@Half-Bloodprince here is the original Euclid's proof of that fact: aleph0.clarku.edu/~djoyce/java/elements/bookXII/propXII10.html
Dec
2
comment Innovation behind formula for surface area and volume of a sphere
@Half-Bloodprince You should be able to find easily the geometric proof that the cone is 1/3 the volume of the circumscribing cylinder.
Dec
2
comment Innovation behind formula for surface area and volume of a sphere
@Half-Bloodprince Also a standardized summation of simple shapes argument. Here is an example of derivation using a method of disks (which I don't like): mathforum.org/library/drmath/view/55263.html
Dec
2
answered Innovation behind formula for surface area and volume of a sphere
Oct
23
awarded  Nice Question
Oct
1
answered Find the point in this line such that the distance from $A$ is $\sqrt{3}$
Oct
1
revised Find the point in this line such that the distance from $A$ is $\sqrt{3}$
added 4 characters in body
Sep
30
awarded  Explainer
Sep
16
awarded  Yearling
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
answered 2 examples to try to understand partials derivatives and deriviability
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
answered Omega Notation and Average Running Time Problem
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.