2,030 reputation
520
bio website
location
age
visits member for 2 years, 4 months
seen 2 hours ago

Squirtle, squirtle......


2d
comment Disprove the statement given below
I hope you are being silly
2d
answered Disprove the statement given below
Aug
18
reviewed Approve suggested edit on Solve $y''-3y'+2y=x^2$
Aug
18
reviewed Approve suggested edit on Is $\dfrac {dy} {dx} = \dfrac {2x} {3y}$ a homogeneous differential equation?
Aug
16
reviewed Approve suggested edit on Uniform convergence of a sequence of polynomial logarithm
Aug
16
comment Proof of “every convex function is continuous”
That's not what I was worried about. Worried about the fact that it was an erv (thought it might fail). But if your erv is an extension of a convex function it's clear it'll be too (where we define the extension as $\infty$ outside the original domain)
Aug
16
comment Fast way to find the sum of LCM of the given range of numbers?
Are you asking me how the computer computes lcm and gcd? Or? Because I don't know how the computer does it, but if the computer needs gcd to do lcm then your method above can't better because allegedly that's how the computer would have to do it anyway. Alternatively, if the computer can independently compute gcd or lcm without the other then your method is actually slower. Either way, your method isn't better.
Aug
16
answered What is the method to correctly isolate $y$ as the dependent variable for $x = e^y$?
Aug
16
comment Proof of “every convex function is continuous”
Well .... I see the function is convex as well (as it should be). I guess I just don't like using e.r.fs (Also in my last comment I should have had $t\ge f(x)$ and $t\in \mathbb{R}$ but the result is the same nonetheless.)
Aug
16
comment Proof of “every convex function is continuous”
Ah! You're right. It is a convex set, because the epigraph to the right of $x=0$ is clearly convex and so now we just have to show that the union of this epigraph with the epigraph when $x\le 0$ is also convex. But epi($f(x):x<0)=\{(x,t):t>f(x)\}=\{(x,t):t>\infty \} = \emptyset$ which makes the desired result vacuously true. The only problem with this example is that we want a function to convex if and only if its epigraph is convex (and we can normally prove this).
Aug
15
comment Proof of “every convex function is continuous”
Real valued function $\neq$ extended real value function (the former is the setting setting of the question and my answer, the latter is your setting). In any case, your epigraph isn't even convex,... for example you can't realize it as the intersection of epigraphs of real valued functions. If you could, then I'd believe it was convex because the intersection of arbitrary number of convex sets is convex... but your set is definitely not convex
Aug
15
comment Proving the completeness of some sets (or disproving it)
The sine and cosine functions are orthogonal in $L^2$ does this help you? So if you just have $A$ and none of $B$ then you can still add elements that linearly independent...
Aug
14
reviewed No Action Needed Mutiply Hexadecimal
Aug
14
reviewed No Action Needed How to calculate limit of a function having factorial in denominator
Aug
14
awarded  Custodian
Aug
14
comment Finding a “big” bounded subset of a subset of $\mathbb R$
Well the result is certainly true if $A$ is bounded... just let $A_1=A$ then $m(A_1^c \cap A) = m(\emptyset)=0$
Aug
14
answered Prove that spec$(f(A)) = f$(spec$(A)).$
Aug
14
comment Prove that spec$(f(A)) = f$(spec$(A)).$
See any book on the subject of functional analysis. Also, you may try Applied Analysis by Hunter and Nachtergaele. This is called the Spectral Mapping Theorem. Its Googleable.
Aug
9
comment Fast way to find the sum of LCM of the given range of numbers?
This is actually a tougher operation since computing $\gcd(i,n)$ is just as tough as computing $lcm(i,n)$ but now you are also including a inversion and multiplication by $i$.
Aug
8
suggested suggested edit on The space $C_b(\mathbb{R})$ is complete