If f has a 4-periodic point $x_1$ st, $x_1<f(x_1)<f^2(x_1)<f^3(x_1)$ show $f$ has a periodic point of any order.
Prove that $T$ has an orbit of period 3
Semicolon or dash? Diamond moderator rollbacks can resurrect blacklisted tags Edit:  Of course my real code doesn't look exactly like this. I tried to write semi-pseudo code to make it more clear of whay I wanted to do.  Looks like it just messed things up instead.  So, what I actually would like to do is this:  Method&lt;Interface1&gt;(); Method&lt;Interface2&gt;(); Method&lt;Interface3&gt;(); ...   Well ... I thought that maybe I could turn it into a loop using reflection. So the question is: How how do I do it. I have very shallow knowledge of reflection. So code examples would be great.  The scenario looks like this:  public void Method&lt;T&gt;() where T : class {} public void AnotherMethod() {     Assembly assembly = Assembly.GetExecutingAssembly();      var interfaces = from i in assembly.GetTypes()     where i.Namespace == "MyNamespace.Interface" // only interfaces stored here     select i;      foreach(var i in interfaces)     {         Method&lt;i&gt;(); // Get compile error here!     }       Original post:  Hi!  I'm trying to loop through all interfaces in a namespace and send them as arguments to a generic method like this:  public void Method&lt;T&gt;() where T : class {} public void AnotherMethod() {     Assembly assembly = Assembly.GetExecutingAssembly();      var interfaces = from i in assembly.GetTypes()     where i.Namespace == "MyNamespace.Interface" // only interfaces stored here     select i;      foreach(var interface in interfaces)     {         Method&lt;interface&gt;(); // Get compile error here!     } }   The error I get is "Type name expected, but local variable name found". If I try  ...     foreach(var interface in interfaces)     {         Method&lt;interface.MakeGenericType()&gt;(); // Still get compile error here!     } }   I get "Cannot apply operator '&lt;' to operands of type 'method group' and 'System.Type'" Any idea on how to get around this problem? What's the fixed size of the suggested edit queue? We know that Stack Overflow has a suggested edit queue, visible to the users who have the  privilege. Someone said the queue has a fixed size.  What's the fixed size of the suggested edit queue?  Is it often that the queue gets filled up and users can no longer suggest edits? Change the location of .bashrc Is it possible to change the location of .bashrc from /home/orhanc/.bashrc to some other directory? In Excel, the window can be frozen in place in such a way that you can always see the name of the column even though you go way down below the 'fold' of the screen.  On SE, when you scroll, the whole page goes up (or down). This means the top navigation bar is scrolled off screen. I'm not sure if it would be a good idea or not to fix the top navigation to the top of the screen and let the rest of the content scroll.  What do you think about this, in terms of pros and cons?  [Update]  With the new Top navigation bar, kudos to the design team, I think this question becomes relevant again. I'm aware of the busload of downvotes, but still.  The top navigation bar doesn't occupy much space and has two notification areas:   Inbox Achievements   Having these two notifications visible at all times would be nice, IMO.  [Update]  I've just noticed that I haven't used the word "optional" in this discussion... My bad. In Excel, the Freeze function is controlled by the user. You can optionally Freeze part of the interface, and you can eliminate the Freeze at will. Subset data frame based on number of rows per group $\Delta U$, $C_p$, $C_v$ for an ideal gas process mknod /tmp/oracle.pipe p  sqlplus / as sysdba &lt;&lt; _EOF set escape on  host nohup gzip -c &lt; /tmp/oracle.pipe &gt; /tmp/out1.gz \&amp; spool /tmp/oracle.pipe select * from employee; spool off  _EOF  rm /tmp/oracle.pip   I need to insert a trailer at the end of the zipped file out1.gz , I can count the lines using  count=zcat out1.gz |wc -l   How do i insert the trailer  T5 (assuming count=5)   At the end of out1.gz without unzipping it. Making tags visible when using a Tumblr theme that doesn't show them Question about Casella and Berger's proof of MLE invariance In Casella and Berger, p. 320, they have a proof of the invariance of the MLE. Let $g: \theta \mapsto \eta$ be a function. They define the induced likelihood as  $$ L^*(\eta \mid X) = \sup_{\{\theta: g(\theta) = \eta\}} L(\theta \mid X). $$  This ensures that $g$ is one-to-one with respect to the likelihood functions because if $g$ is not one-to-one, there may be multiple values of $\theta$ that map to a given $g(\theta) = \eta$.  Then they note  $$ \sup_{\eta} L^*(\eta \mid X) = \sup_{\eta} \sup_{\{\theta: g(\theta) = \eta\}} L(\theta \mid X) = \sup_{\theta} L(\theta \mid X). $$  The first equality just applies the definition of the MLE of $\eta$. However, the next inequality confuses me. They write,     The second inequality follows because the iterated maximization is equal to the unconditional maximization over $\theta$...   Can someone justify this claim or provide some intuition if the claim is supposed to obviously follow from definitions? I'm printing a tradeshow flyer and was wondering what type of paper I should print it on. I don't want anything glossy so I'm trying to decide on the following:   100# text weight matte 80# cover 80# matte   What is the difference between the types above? And how can I make a decision? Grandi's Series; tends to $1/2$, but why is this considered a valid sum? If derivative of function is less than or equal to 4, prove the existence of point $c$ so $f(c)=c^2$. I am struggling to construct a simple proof of the following.  Suppose $f(x)$ is differentiable for any real value $x$ and that $f'(x) \le 4$ for all real values of x. Prove there is at most one real value $c&gt;2$ such that $f(c) =c^2$.  I am completely lost on where to start on this proof and any help would be greatly appreciated! Please clarify how entropy increases when matter gravitationally coalesces On John Baez's website, , he discusses the problem of how entropy increases when a cloud of ideal gas collapses gravitationally (no black holes - keeping it simple).  But he doesn't give away the answer - instead he implies that, I presume, either gravitons or photons are released during collapse and these increase the overall system entropy.  Can someone please answer which it is, gravitons or photons?  If gravitons (or gravity waves), then does this mean that pre-20th century physicists, with no notion of gravity waves, would have concluded that gravitational attraction violates the 2nd law?  And if photons, then what about if the gas particles were totally neutral - wouldn't they not emit any EM radiation in that case?  Or am I wrong that gravitons or photons are the answer? Thanks! Proof of Dobinski's formula for Bell numbers When do exactly we choose to use have or take? They look sort of having similar context     I have a bath      I take a bath   And by the way, I saw that      I take a chance   Can't be transformed to     I have a chance   Can it?   *Moreover, If there's a verb used like the bath, it means the bath is no more a verb but a noun right?  Also very important is that , can they be applied randomly to *a verb or a noun?  Like :  *  - I take a choose   Or    I take an option ( this one makes sense but I mean in the context of delexical verb)   ?  *EDIT: My mistake , bath is actually not "a verb transformed to a noun, but its absolutely a noun."  So my concerns would be if they can be used interchangeably? And be applied to random noun? Linking search box to dataset column in Carto? The search box in a published map of CartoDB isn't linked to the dataset which is shown in the CartoDB map. How can I link the search box to a certain column of a dataset? I am currently working to design a flash virtual tour, but I know little about how the photographs are taken.  Ideally I'd like to be able to take a set of 6 shots from a single focal point, and be able to align them seamlessly into a cube form. The other solution is to take a special fisheye image, and stretch it dynamically in flash.  I've seen examples of both as virtual tours, and ones formatted as a rotating cube are more responsive and have a higher image quality. The airbus and Cruden Homes are definitely in the cube format, I'm not entirely certain which format the New York VT uses:        I have a set of questions, the first is the most important, the others may become separate questions if I don't get an answer here:   How are those photos taken? Is there a specific mount that can be used? How long does it take to set up? How much post-processing is necessary on the images? Ifstream read function doesn't load into vector