Sugar daddy asked me to send $29 to his account manager's PayPal
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How do I check the integrity of a storage medium (hard disk or flash drive)? I've run across (personally or by proxy) a bunch of storage media that exhibited physical problems during their life. Hard disks, solid state drives and other flash storage media all fail after some time. The situation is worse with USB flash drives and flash cards because of the large amount of suppliers with inferior flash cell and flash controller quality.  How can I reliably detect if a storage drive suffers from physical damage?  Note that this question isn't about file system integrity (which can be checked with ). Setting-up SSH-tunnel for VPN? I have a laptop running Ubuntu.  I also rent a VPS running Ubuntu.  I've bought a paid VPN-service, which I use on my laptop.  I was wondering how I can set-up a SSH-tunnel or something similar, from my laptop to the VPS I'm renting, so I then can run VPN (from my laptop) "through" it (to the VPS), to the VPN-server.  The reason I wish to do so, is that a place I often work blocks my VPN-service, but not my SSHing to my VPS...  While I have been using Linux for a while, I'm a novice when it comes to setting-up virtual network-devices, advanced routing, and so on... so please spoonfeed me (using small words and colorful pictures ;-)  I have been googling and looking at various answers on the StackExchange-network, but not seems to be exactly what I'm after.  SSH-tunneling seemed promising, but since I don't have/know an exact domain and port for my VPN, I couldn't figure out how to use it...  I guess I may need to set-up some virtual network-device on my laptop (which ends on the VPS), and connect VPN through it - but how to do this, sadly goes over my head. Using proof by contradiction vs proof of the contrapositive Constructor not defined error in test code Basically this suggestion for the Android app:   Many times I'll see that a post has been edited on the Android app. I'll want to see exactly what was edited, and the Android app doesn't show this. Can the revision history be added to the Android app? How to show that $\lim \frac{1}{n} \sum_{i=1}^n \frac{1}{i}=0 $? Show that  $$\lim \frac{1}{n} \sum_{i=1}^n \frac{1}{i} =0 $$  I've proved that this sequence converges (it is bounded and decreasing). NOW, I need to find a sequence that is bigger than this one and goes to zero. Maybe something using geometric serie of 1/2  Thanks in advance! Let $G = \mathbb{R} / \mathbb{Q}$. Is this an interesting group to study?  Is it isomorphic to any more natural mathematical objects? Let $T,S$ be linear transformations, $T:\mathbb R^4 \rightarrow \mathbb R^4$, such that $T^3+3T^2=4I, S=T^4+3T^3-4I$. Then S is:   one-one but not onto onto but not one one invertible non-invertible   (One or more correct options)  My attempt: $S=T^4+3T^3-4I=T(T^3+3T^2)-4I=T(4I)-4I=4T-4I$  How do I go about proving or disproving my options?   My thoughts on options # 1. and 2.: I'm guessing $S$ is one-one if $Ker(S)=\theta$ is one way to go, but how do I obtain the kernel when I don't know what the transformation is? $Ker(S)=\theta$ if $T=I$, which does satisfy $T^3+3T^2=4I$. But so can other $T$s.   My thoughts on options # 3. and 4.: $S$ is invertible if $det(S)\neq0$, which is possible $det(T-I)\neq0$, i.e. $T\neq I$. How do I show that?  Please help! How to use more than 10 tab stops in bmatrix or other amsmath matrix environments? Why does changing the returned variable in a finally block not change the return value? Supposing to have something like this:  #include &lt;map&gt; int main(){     std::map&lt;int,int&gt; m;     m[1] = 2;     m[2] = 4;     return 0; }   I would like to be able to inspect the contents of the map running the program from gdb. If I try using the subscript operator I get:    (gdb) p m[1] Attempt to take address of value not located in memory.   Using the find method does not yield better results:  (gdb) p m.find(1) Cannot evaluate function -- may be inlined   Is there a way to accomplish this? What is the word for when someone is overly nice and actually isn't nice at all because of the unnecessary added information/comments? For example, they will say things like "Your hair looks so good that wayyyy omg you should do it that way ALL the time! Looks way better than how you usually do it." And the word I'm looking for is not passive aggressive and it is not sarcasm. There is a word for these types of people. What is it? These people think they're being kind but actually blunt and rude. Another example would be for someone to say "hey you're beautiful, but maybe if you didn't wear harsh makeup you would look better" and they intend to sound like they're being nice when you know they don't like you and are saying in out of spite. Using .NET, how can you find the mime type of a file based on the file signature not the extension Any Set with Associativity, Left Identity, Left Inverse is a Group I'm finishing professional school and over the years have acquired a pile of notes and articles that I'd like to hang onto.  I'd like to add to them and create sort of an archive of article and files that may be useful down the road.  I'd also like to organize this collection of files not only by simple grouping but also with tags.  I feel like that will make searching through them years later much easier.  Suggestions on software that would be good for this?  Just a general file manager, something that uses tags that can be attached to each file? Variation of Pythagorean triplets: $x^2+y^2 = z^3$ I have to prove this : "$n^7-n$ is a multiple of 7". This is what I have done this so far :  $P(n):n^7-n$ On putting $n=1,$ $P(1):1^7-1=0$, which is a multiple of 7. So, $P(1)$ is true. Let $P(k)$ be a multiple of 7. So, $k^7-k$ is a multiple of 7. So, $k^7-k=7m$, where $m$ is any natural number. Let $P(k+1)$ be true, Hence, $(k+1)^7-(k+1)$ is a multiple of 7.  Now, how do I evaluate $(k+1)^7$ without using the binomial theorem ? Or is there some other way to do it ? Exercise 3.5.12. Let $ f: \mathbb N \times \mathbb N \to \mathbb N$ be a function, and let c be a natural number. Show that there exists a function $a:\mathbb N\to \mathbb N$ such that $$a(0)=c$$ and $$a(n++)=f(n,a(n))\;for\;all\;n\in \mathbb N,$$ and furthermore that this function is unique. Tao gives the hint: first show inductively, by a modification of the proof of Lemma 3.5.12, that for every natural number $N\in \mathbb N$, there exists a unique function $a_N:\{ n\in \mathbb N:n\lt N\}\to \mathbb N $ such that $a_N(0)=c$ and $ a_N(n++)=f(n,a(n))$ for all $n\in \mathbb N$ such that $n\lt N$.  In my opinion, we could solve it by proving that $\forall n\in \mathbb N,a(n)\in \mathbb N$ according to mathematcial induction.  The property P(n) is:$$\forall n\in \mathbb N, a(n)\;is\;unique$$ P(0) is true. And if P(n) holds, P(n++) is true because different natural numbers must have different successors. $$a(n++)=f(n,a(n))$$ $$a(m++)=f(m,a(m))$$ $$n++=m++\Rightarrow n=m\Rightarrow a(n++)=a(m++)$$ It's similar to the proof of  Proposition 2.1.16 (Recursive definitions): Suppose for each natural number $n$, we have some function $f_{n} : \mathbb{N} \rightarrow \mathbb{N}$ from the natural numbers to the natural numbers. Let $c$ be a natural number. Then we can assign a unique natural number $a_{n}$ to each natural number $n$, such that $a_{0} = c$ and $a_{n{++}} = f_{n} (a_{n})$ for each natural number $n$.  This proof indicates both the existence and uniqueness of the function $a$. I don't know why Tao says it's informal.  But regarding the hint, how do we get the function f even if we've got the conclusion from the hint. Also it seems like the function a(n) can be diffentent considering different N. I don't know if the hint is correct. Unbiased estimator of a uniform distribution I'm reading the Algebra book by Knapp and he mentions in passing that an orthonormal set in an infinite dimension vector space is "never large enough" to be a vector-space basis (i.e. that every vector can be written as a finite sum of vectors from the basis; such bases do exist for infinite dimension vector spaces by virtue of the axiom of choice, but usually one works with orthonormal sets for which infinite sums yield all the elements of the vector space).  So my question is - how can we prove this claim? (That an orthonormal set in an infinite dimension vector space is not a vector space basis).    Edit (by Jonas Meyer): Knapp says in a footnote on  of Basic algebra:     In the infinite-dimensional theory the term "orthonormal basis" is used for an orthonormal set that spans $V$ when limits of finite sums are allowed, in addition to finite sums themselves; when $V$ is infinite-dimensional, an orthonormal basis is never large enough to be a vector-space basis.   Thus, without explicitly using the word, Knapp is referring only to complete infinite-dimensional inner product spaces.