In the past, i.e. a billion years ago, if the universe is larger than our observable universe, would there have been more objects in our observable universe that have now accelerated beyond it?
After a very long time will we see more stars (due to the fact that more light is get to us) or less stars (as the universe expends and light have to pass larger distance)? In general, can stellar objects go outside of the scope of the observable universe or is it only growing with time? Calculations are always better than just discussion. Does it have any connection to dark matter?
The Challenge  I have been trying to write a filter that applies (prepends a string) to (a) post titles of a certain post type and (b) to that same post type WordPress admin backend for use by an auto social sharing plugin.  I've gotten really close.  I've achieved: 1.  prepending only to custom post_type post titles 2.  prepending to custom_post type titles AND all nav menu items 3.  prepending to ALL titles (post, page, nav menu, and backend auto-sharing plugin)  The final, 3rd attempt got me very hopeful, but yet still, no matter the function, conditional statement, or combination I use, I can't get custom_post title AND backend social sharing plugin, but not nav menu items.  My Code - what I've tried  I've tried different conditionals, like is_admin() and !is_nav_menu with all nav menu IDs.  I've also tried comparing the ID of the post to the ID of the menu.  Finally, I've also tried adding the filter only to loop_start and that seems promising if combined with other statements.  I will clean up my code for your review but I leave it this way for now in hopes it helps to see what I've tried and maybe where I went wrong with any of those methods.  // , $id = NULL function append_album_review_to_title( $title ) {     global $post;     global $dont_apply_title_filter;     $text = 'Album Review: ';     $prepended_title = $text . $title; /*     $nav_menus_obj = wp_get_nav_menus();     $nav_menu_ids = '';     foreach( $nav_menus_obj as $nav_menu ) {         $nav_menu_ids .= $nav_menu-&gt;term_id . ',';     }     rtrim($nav_menu_ids, ','); */ //  if ( get_post_type( $post-&gt;ID ) == 'album_review' &amp;&amp; in_the_loop() ){ //  if ( get_post_type( $post-&gt;ID ) == 'album_review' &amp;&amp; $id == get_the_ID() ){ //  if ( !is_nav_menu( '32057,32058,35135,32054,32056' ) ) { //  if ( get_post_type( $post-&gt;ID ) == 'album_review' &amp;&amp; is_nav_menu( $id ) ) {     if ( get_post_type( $post-&gt;ID ) == 'album_review' &amp;&amp; !$dont_apply_title_filter ) {         //print_r( $nav_menu_ids );         //print_r( is_nav_menu( $nav_menu_ids ) );         return $prepended_title; /*     } elseif ( get_post_type( $post-&gt;ID ) == 'album_review'  ) {         return $title; */     } else {         return $title;     }; } add_filter('the_title', 'append_album_review_to_title'); //add_action('save_post', 'custom_post_type_title', 100); /* function set_custom_title() {     add_filter( 'the_title', 'append_album_review_to_title', 10, 2 ); } add_action( 'loop_start', 'set_custom_title' ); */ How can I install .ipa file to my iPhone simulator? I need to install .ipa file to my iPhone simulator.   I tried to change the extension .ipa to .zip and extracted it.  And I got the Payload folder and moved the application inside to my iPhone simulators applications folder found at: /Library/Application\ Support/iPhone Simulator/6.1/Applications/.   Application appears on iPhone Simulator, But the application did't running. How to solve the problem then how to run the app. In Rey's vision, whose voice says "These are your first steps"? Is there a difference between a LED Backlit and LED HD  Display on laptop monitor? or are they the same that is good for the eyes Consider the following MWE:  \documentclass{article} \usepackage{pstricks} \begin{document} A \end{document}   It produces the error  Runaway argument? ] {pgffor.code.tex}  ! Paragraph ended before \ProvidesPackageRCS@i was complete. &lt;to be read again&gt;                     \par  l.11   How do I fix this? Proving the measure of an increasing sequence of measurable sets is the limit of the measures Show that if $A_1\subseteq A_2\subseteq A_3\subseteq\cdots$ is an increasing sequence of measurable sets (so $A_j\subseteq A_{j+1}$ for every positive integer $j$), then we have $$m\left(\bigcup_{j=1}^\infty A_j\right)=\lim_{j\to\infty}m(A_j)$$  Here is my proof: According to the $\sigma$-algebra property, $\bigcup_{j=1}^{\infty}A_j$ is a measurable set, so it makes sense to talk about $m(\bigcup_{j=1}^{\infty}A_j)$. Firstly, I prove that $\lim_{j\to\infty}m(A_j)\leq m(\bigcup_{j=1}^{\infty}A_j)$. This is because for any given positive integer $N$, $A_N\subseteq \bigcup_{j=1}^{\infty}A_i$, according to monotonicity, we have $m(A_N)\leq m(\bigcup_{j=1}^{\infty}A_i)$. Take the limit,we will have $\lim_{j\to\infty}m(A_j)\leq m(\bigcup_{j=1}^{\infty}A_j)$. Secondly, I prove that $m(\bigcup_{j=1}^{\infty}A_j)\leq \lim_{j\to\infty}m(A_j)$. For any given positive integer $N$, $\bigcup_{j=1}^N A_j = A_N$. According to monotonicity,we have $m\left(\bigcup_{j=1}^N A_j\right)=m(A_N)\leq \lim_{j\to\infty}m(A_j)$. Take the limit, we will have $m\left(\bigcup_{j=1}^\infty A_j\right) \leq \lim_{j\to\infty} m(A_j)$. Combine the above two arguments, we will see that $$m\left(\bigcup_{j=1}^\infty A_j\right)=\lim_{j\to\infty} m(A_j)$$$\Box$  The above is my proof, unlike many books, my proof does not use the property of countable additivity. So I doubt my proof is correct. Who can point out where are my mistakes? Is there a name for an element $z$ such that $\,zx = z = xz\,$ for all $x$? Is there a general name for the following properties, (similar to the properties of existence of an additive identity, existence of multiplicative identity etc):   For any given set, the intersection with the empty set results in the empty set. For any real number, multiplication with zero results in zero. Why does a cordless circular saw have the blade on the left? At the moment considering the purchase of a circular saw for light work. I'm looking at a corded model and a cordless model. But the question I have is not about which one is better.   My question today is why the corded one has the blade on the right of my hand and the cordless one has the blade on the left of my hand. See both models below.     Now, I know some manufacturers make left- and right-handed versions of their circular saw. And I'm also aware that 'worm drive circular saws' usually have the blade to the left of my hand. But it seems odd to me. Especially as it seems to apply to most manufacturers too.   Was wondering if somebody has an explanation for this. Invalid SSL certificate when pushing to Git server Is “all women who are mothers of daughters” right? Is the expression      All women who are mothers of daughters are here.   correct? I mean every woman who has at least one daughter is here. How is a second measured? And why is it measured that way? The earth's rotation around itself (one rotation around Earth's own axis) doesn't take exactly 24 hours. It off by some seconds which becomes somewhere around 6 hours per year and 1 day in 4 years(leap year), which brings the question why didn't we modify the measurement of 1 second ever so slightly so as to avoid leap years altogether.   Well how is 1 second measured exactly?  says      the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom. []   Well, why is it measured that way? Is there any technical reason like it is easy to measure and can be standardized easily? Or is it really possible to modify the measurement of time? How does a sarlacc gain any energy if it keeps victims alive for a thousand years? When eaten by a sarlacc, according to C-3PO,     In his belly, you will find a new definition of pain and suffering, as you are slowly digested over a thousand years.   I imagine that keeping a victim alive for a thousand years takes much more energy than is available to the sarlacc from the body of the victim.  Thus, keeping victims alive for so long would seem to be a net loss of energy for the sarlacc.  Is there a canon answer to resolve this conundrum?  Did the sarlacc have another energy source (for example, ability to harvest sunlight)? I have a MacBook Pro Retina (2015). After updating to OS Mojave, Bluetooth has stopped working. I get an error message that "No Bluetooth Hardware Found".  I have already tried to do the following:   Go to the /Library/Preferences and delete the com.apple.Bluetooth.plist file Successfully resetting SMC. (pressing Shift+ctrl+alt + power button) Removing the Bluetooth icon from the menu bar    None of the above solutions has worked for me. What can I do when getting "We are no longer accepting questions/answers from this account"? Is there a way to load my own custom CSS or Javascript while using a browser?  When I'm accessing a website or developing a website I want to load my own custom scripts from my computer. I know this can be done by Firebug or Chrome's developer toolbar, but after you refresh your browser your changes will be cleared too. This is exactly what I'm looking for adding CSS and Javascript, but I wish it has an option where you temporarily save your changes locally. Or it has an option to load external CSS or JS files.   Purpose:   When I'm developing the frontend, sometimes it's convenient for me using Chrome's developer toolbar or Firefox's Firebug to change or tweak CSS properties because I can then see the changes in real time without refreshing. One problem I see is that every time I refresh my browser, my changes also get reset. Now I wish there were an option where I could save my changes locally or load my own external .css file or .js file. I want to customize how some websites look when viewed locally, e.g., accessing a blog that has too many ads. I want to apply CSS properties to hide the junk.   Browsers I use often:   Google Chrome (for development: Built-in Dev Toolbar) Mozilla Firefox (for development: Firebug) Today I was informed by VFS that my tourist visa for UAE got approved. I'm travelling to UAE on 16th December 2014 and returning on 7th Jan 2015. But when I checked the "valid until" date on the visa it states 30 December 2014.    Does this date mean I should return before December 30th? Should I get it corrected from VFS? glBufferData not working outside main function Why did sampling boost the performance of my model? I have an imbalanced dataset with 88 positive samples and 128575 negative samples. I was reluctant to over/undersample the data since it's a biological dataset and I didn't want to introduce synthetic data. I built a Random Forest Classifier with this original dataset. I got an F1 score of 0 for the positive class. Zero precision. Zero recall. I cross-checked the predictions and test data. The model predicts some positives none of which are actually positive. Worst performance.  So, I tried to oversample the positive class. I upsampled the positives to 1000 samples. To my surprise, the F1 score for this dataset was 0.97, for the positive class. Then I tried lesser samples. I was able to achieve an F1 score of 0.83 with 200 positive samples, which is just 2.25 times of the original positive samples.  I would like to know why this occurs. For 88 samples, F1 score is 0.00 (rounded off to two digits). For 200 samples it's 0.83. There is no data leakage. All the features are engineered. I used imbalanced-learn module for oversampling. Can someone explain why is this difference in performance? Less than or equal sign If I know for two numbers a and b that    $${a &lt; b }$$  Then is it correct to say that    $$ a \leq b $$  I know that the second statement is true as long as the first one is. It seems OK as it is true but from the other side it seems kinda weird (to me), to say that, if you know, that a is strictly less that b.It's like you lose some extra information. Where is the New Oxford American Dictionary stored?