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$y_{2n}, y_{2n+1}$ and $y_{3n}$ all converge. What can we say about the sequence $ y_n$? My friend and I are currently debating the following question:      Let $y_n$ be a sequence in a metric space and assume that the subsequences    $y_{2n}$, $y_{2n + 1}$, and $y_{3n}$ all converge. What can we say about the sequence $y_n$?    To me it seems that all the subsequences will converge to a limit say $y$. Then any term in the original sequence will be in one of these subsequences, it follows that the entire sequence $y_n$ converges to $y$.  I let $\varepsilon &gt; 0$. Since $y_{2n}$ converges to $y$ there exists an index $2N$ such that $d(y_{2n},y) &lt; \varepsilon$ for $2n \geq 2N$, and since $(y_{2n+1})$ converges to $y$ there exists $2M + 1$ such that $d(y_{2n+1}, y) &lt; \varepsilon$ for $2n + 1 \geq 2M + 1$.  Let $m \geq \max\{2N,2M+1\}$. If  $m$ is even, since $m\geq 2N$ we have $d(y_m,y)&lt;\varepsilon$; if $m$ is odd, since $m\geq 2M+1$ we have $d(y_m,y)&lt;\varepsilon$. Thus $d(y_m,y)&lt;\varepsilon$ for any $m \geq \max\{2N,2M+1\}$, and we conclude that $(y_n)$ converges to $y$.   However, my friend does not think that this is completely correct because I didn't use the $y_{3n}$ in the proof. I think he is right, that I do in fact need it, but I am unsure of how to add it in. All in all, I think that since any term in the original sequence will be in one of these subsequences, it follows that the entire sequence $(y_n)$ converges to $y$.  $2n+1$ covers all the odd terms and $2n$ converse all the even terms, so is $3n$ even needed? I would like to use it since the proof has it in the question, but I am unsure of what to do. Could someone kindly help me construct this proof in a better manner,and is my line of thinking correct? Thank you! What IDE to use for Python? I need help finding the set of continuous functions $f : \Bbb R \to \Bbb R$ such that for all $x \in \Bbb R$, the following integral converges:  $$\int_0^1 \frac {f(x+t) - f(x)} {t^2} \ \mathrm dt$$  I think it might be the set of constant functions but i havent been able to prove it :(   I was thinking that you can use the stone weiestrass theorem considering the set of continuous functions on a closed  interval(non trivial) ,and a subset which contains the set of continuous functions whose integral above diverges in some point in that interval along with  with the set of constant functions. So in order to solve the problem i need only to prove that if two functions do not meet the condition of the problem then their product does not as well .  I hope you can provide some insight and thank you . 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Here is my code syntax that I am attempting to use:  Email Code:  &lt;p&gt;&lt;a title="MyPage" href="%%=RedirectTo(CloudPagesURL(505,'Email Address',@EmailAddress))=%%" alias="ThisAlias" conversion="false"&gt;Click to unsubscribe page 505&lt;/a&gt;&lt;/p&gt;   CloudPage AMPScript Code:  %%[  VAR @emailAddress  SET @emailAddress = RequestParameter("emailaddr")  ]%%   Cloudpage HTML Code:  &lt;td width='155' valign='bottom'&gt;&lt;input type='text' name='Name1' value='%%=v(@emailAddress)=%%' id='Name1' /&gt;&lt;/td&gt;   Any reason as to why this doesn't work? My syntax might just be wrong or I might be using the CloudPagesURL() function incorrectly. Dynamically Create a generic type for template I'm programming WCF using the ChannelFactory which expects a type in order to call the CreateChannel method. For example:   IProxy proxy = ChannelFactory&lt;IProxy&gt;.CreateChannel(...);   In my case I'm doing routing so I don't know what type my channel factory will be using. I can parse a message header to determine the type but I hit a brick wall there because even if I have an instance of Type I can't pass that where ChannelFactory expects a generic type.   Another way of restating this problem in very simple terms would be that I'm attempting to do something like this:  string listtype = Console.ReadLine(); // say "System.Int32" Type t = Type.GetType( listtype); List&lt;t&gt; myIntegers = new List&lt;&gt;(); // does not compile, expects a "type" List&lt;typeof(t)&gt; myIntegers = new List&lt;typeof(t)&gt;(); // interesting - type must resolve at compile time?   Is there an approach to this I can leverage within C#? How do you compile OpenSSL for x64? After following the instructions in INSTALL.W64 I have two problems:   The code is still written to the "out32" folder. I need to be able to link to both 32-bit and 64-bit versions of the library on my workstation, so I don't want the 64-bit versions to clobber the 32-bit libs. The output is still 32-bit! This means that I get "unresolved external symbol" errors when trying to link to the libraries from an x64 app. Iphone 4 won't update past a 7.1.2 I have a IPhone 4  model number A1349 an it won't update past a 7.1.2 it says my software is up to date but I know the latest software is at the least a 8.4.  Why is that? SQL Server equivalent to Oracle's CREATE OR REPLACE VIEW rsync a file from serverC to serverA through serverB Fusion: Why deuterium and tritium? I would like to know why scientists try to use deuterium and tritium for  and not just the ordinary  ${}^1H$? I have a site that is in French and English. I am able to successfully setup so that users can switch back and forth between the two domains to view either language, however I cannot seem to keep users logged in. When they are logged into the english domain and then switch to the french domain they are required to login again. However if they switch back to the english domain they are still logged in.  As an example we'll use www.english-domain.com as the base (default) domain and www.french-domain.com as the secondary domain  In settings.php I have modified the following, however it doesn't seem to be keeping them logged in. Am I missing something?  /**  * Drupal automatically generates a unique session cookie name for each site  * based on its full domain name. If you have multiple domains pointing at the  * same Drupal site, you can either redirect them all to a single domain (see  * comment in .htaccess), or uncomment the line below and specify their shared  * base domain. Doing so assures that users remain logged in as they cross  * between your various domains.  */ $cookie_domain = 'english-domain.com';   Note: That I have also flushed both site and browser cache as well as deleted any cookies left on my machine.  Update:  Here are my language settings: Density of finite rank operator in compact operators on Hilbert spaces Why on the first page Google says there are thousands of results but on the last page there are less than a hundred? How to customize the package editor interface? I was given this problem 30 years ago by a coworker, posted it 15 years ago to rec.puzzles, and got a solution from Barry Wolk, but have never seen it again.  Consider the series:  $$1, \frac{1}{2},\frac{\displaystyle\frac{1}{2}}{\displaystyle\frac{3}{4}},\frac{\displaystyle\frac{\displaystyle\frac{1}{2}}{\displaystyle\frac{3}{4}}}{\displaystyle\frac{\displaystyle\frac{5}{6}}{\displaystyle\frac{7}{8}}},\cdots$$  Each fraction keeps its large bars while being put atop a similar structure. This can also be represented as $$\frac{1\cdot 4 \cdot 6 \cdot 7 \cdot\cdots}{2 \cdot 3 \cdot 5 \cdot 8 \cdot\cdots}$$ terminating at $2^n$ for some $n$, where it is much closer to the limit than elsewhere.  The challenge:   Find the limit, not too hard by experiment In the last expression, find a simple, nonrecursive, expression to say whether $n$ is in the numerator or denominator Prove the limit is correct-this is the hard one. $\sqrt{7\sqrt{7\sqrt{7\sqrt{7\sqrt{7\cdots}}}}}$ approximation I’m looking for an adjective/ noun that describes a person who loves life, traveling, great food, always doing things which gets adrenaline kicking and is a always ready for attempting things for pleasure only Now that the , I've been seeing tag-only suggested edits from 1500-rep users.  For example, one had the summary of 'burninating [tagThatWasRemoved]'.  It's very tempting to reject these as Too Minor, but I know that these users used to have a Retag privilege (and are obviously trying to participate in a burnination.)  What should we do for tag-only edits from high(er) rep users? I want to model the transfer function of a resistor mathematically, and am after some resources / tips on if it's possible to do so.  For example, if I put 1V into a 1 Ohm resistor, I want to know how long and how (shape) it will take to reach a steady state temperature, given 25 deg C ambient.  I.e.   $$ \frac{T(s)}{V(s)} = ??? $$  Where T(s) is the laplace transform of temperature T(t), measured in say Kelvin.  I understand there are a lot of factors which will affect this model (material, size, shape, ambient (?)), but I'm not sure where to even start. A  shows the heat rise at a certain load, but not really how it gets there. I can't find a time-domain function for the temperature rise either.