Entropy  As per the second law of thermodynamics  "Order tends to disorder" And recently I watched a video series by minute physics   As per that with increasing time there will be increasing entropy. And therefore it is said:- As time progresses we will be left with just empty space, Thus based on the above information I would like to ask  1)thus the big crunch of the ending of the universe cannot take place! 2)how did the big bang infinitely small point come into play! ???
I recently read that:     What our current level of thermodynamics does tell us though is that if there is such a thing as a Big Crunch, the universe will look a lot different as it heads towards collapse than it did when expanding – the universe started in a state of low entropy and high order and will end in a state of high entropy and   low order.   But shouldn't the order be in a high state and hence entropy becomes a low state in the Big Crunch (assuming a closed universe)?  The reason I write this is because the gravitational forces in a closed universe are so strong they will cause gravitational collapse so the universe will shrink and go backwards, eventually through all the stages of the big bang and become a singularity once more.   It was my understanding that a singularity has a state of high order and low entropy. Have I got this the wrong way round?   If so; Can someone please explain why?
What finite groups always have a square root for each element? Is Highschool of the Dead on hiatus again? The coefficient of $x^9$ in the expansion of $(1+x)(1+x^2)(1+x^3)...(1+x^{100})$.  I tried the following concept, how to sum 9 using 1-9 only without repetition.  1:9, 2:1+8,3:7+2, 4: 6+3, 5: 5+4,  6:1+2+6 ,7:1+3+5, 8:2+3+4  The answer is 8.  How will it be solved using Binomial theorem. Best word wrap algorithm? Word wrap is one of the must-have features in a modern text editor.  How word wrap be handled? What is the best algorithm for word-wrap?  If text is several million lines, how can I make word-wrap very fast?  Why do I need the solution? Because my projects must draw text with various zoom level and simultaneously beautiful appearance.  The running environment is Windows Mobile devices. The maximum 600&nbsp;MHz speed with very small memory size.  How should I handle line information? Let's assume original data has three lines.  THIS IS LINE 1. THIS IS LINE 2. THIS IS LINE 3.   Afterwards, the break text will be shown like this:  THIS IS LINE 1. THIS IS LINE 2. THIS IS LINE 3.   Should I allocate three lines more? Or any other suggestions? ­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­­ Should I upgrade to the "mainline" kernels? Why don't we define division by zero as an arbritrary constant such as $j$? Why don't we define $\frac 10$ as $j$ , $\frac 20$ as $2j$ , and so on? I know that by following the rules of math this eventually leads to $1=2$ , but we could make an exception and say that $j$ is the only number such that $0*j \not= 0$ , and put other restrictions necesary so that we don't get contradictions. We do this for $i$ , so why can't we do it here? For example, $i^2$ , is defined as $-1$ , but you could also say $i^2=\sqrt {-1} *\sqrt {-1}=\sqrt {(-1)(-1)}=\sqrt{1}=1$ , but we make an exception for this. how to create shortcode in wordpress So I have the following code:   &lt;span class="delete"&gt;&lt;a onclick="return confirm('Are you sure?');" href="&lt;?php echo wp_nonce_url( add_query_arg( array( 'action' =&gt; 'my-delete-product', 'product_id' =&gt; $post-&gt;ID ), my_get_navigation_url('products') ), 'my-delete-product' ); ?&gt;"&gt;&lt;?php _e( '삭제', 'my' ); ?&gt;&lt;/a&gt; | &lt;/span&gt;   It is a simple button.  I want to make this into a shortcode so that I can use it anywhere where appropriate.  Any suggestions?  Thanks. 'apt-get' always fails with ERROR 404: Not Found over a package (flashplugin-downloader) the following error is preventing me from installing anything on Xubuntu 11.10. How can I fix it??  $ sudo apt-get install meld Reading package lists... Done Building dependency tree        Reading state information... Done meld is already the newest version. 0 upgraded, 0 newly installed, 0 to remove and 0 not upgraded. 1 not fully installed or removed. After this operation, 0 B of additional disk space will be used. Do you want to continue [Y/n]? Y Setting up flashplugin-downloader (11.0.1.152ubuntu1) ... Downloading... --2012-02-06 21:23:36--  http://archive.canonical.com/pool/partner/a/adobe-flashplugin/adobe-flashplugin_11.0.1.152.orig.tar.gz Resolving archive.canonical.com... 91.189.88.33 Connecting to archive.canonical.com|91.189.88.33|:80... connected. HTTP request sent, awaiting response... 404 Not Found 2012-02-06 21:23:36 ERROR 404: Not Found.  download failed The Flash plugin is NOT installed. dpkg: error processing flashplugin-downloader (--configure):  subprocess installed post-installation script returned error exit status 1 Errors were encountered while processing:  flashplugin-downloader E: Sub-process /usr/bin/dpkg returned an error code (1) Parsing JSON with Unix tools Inequality involving $\limsup$ and $\liminf$: $ \liminf(a_{n+1}/a_n) \le \liminf((a_n)^{(1/n)}) \le \limsup((a_n)^{(1/n)}) \le \limsup(a_{n+1}/a_n)$ Prove that for every $a, b\in R\setminus\{0\}$ is correct this inequality:  $$\frac{|a+b|}{1+|a+b|}&lt;\frac{|a|}{1+|a|}+\frac{|b|}{1+|b|}.$$ Why are polymorphic values not inferred in Haskell? Should the network use thousands separators in numbers? How do I diff two text files in Windows Powershell? I have two text files and want to find the differences between them using Windows Powershell. Is there something similar to the Unix diff tool available? Or is there another other way I haven't considered?  I've tried compare-object, but get this cryptic output:  PS C:\&gt; compare-object one.txt two.txt  InputObject                                                 SideIndicator -----------                                                 ------------- two.txt                                                     =&gt; one.txt                                                     &lt;= How to sort two lists (which reference each other) in the exact same way The close dialog says there are two off-topic votes, but none of the off-topic reasons have votes next to them I've found strange behavior when closing this  - I definitely see that there are 3 closing votes and 2 of them are at "Off-topic" section:   -but there are no explanations on section itself:   -while, normally, it's expected that it will appear. In custom comments section there are also no closing-votes displayed.   Perhaps it's just my browser (which is FF 26 x64 under Win) - so marking this as a "possible bug". Thank you for your attention. More than one private key for RSA In an RSA-encryption scenario, Bob's public key pair $(n, e)$ is $(143, 43)$. An attacker Mallory tries brute-force and comes to $d = 7$ as the private key. The value of $φ(143) = 120$ is not known to Mallory. However from $43 \cdot d \equiv 1 \bmod 120)$, one can calculate the first positive element $d = 67$ from multiplicative group $d = 120 + 67n$ and $n \in \mathbb{Z}$ $d = 7$ clearly doesn't fit in that multiplicative group, so how come it can successfully decrypt the encryption? It's not clear to me how to choose Spells Known when creating a new character at a higher level.  Let's take the Bard as a working example first:  Bard level 2:   Spells Known: 5 Slots per Spell level: 1st &times; 3   Bard level 3:   Spells Known: 6 Slots per Spell level: 1st &times; 4, 2nd &times; 2   I'm interpreting this to mean that, if an existing 2nd-level Bard gains a new level (level 3), he's gaining 1 (one) new spell known. He can then choose the new spell known to be either 1st or 2nd, correct?  What I don't understand then, is the case of creating a new character starting at a higher level; say, creating a new Bard at level 3.  In that case you're forced to choose 6 spells, which must be from the list of 1st- and 2nd-level spells, correct?  When making this 3rd-level Bard from scratch, though, can I select 2nd level spells for all 6 spells known?  As another example, say you're creating a very high level Bard from scratch, starting at level 15. The book says your Spells Known is 19, and your spell slots are 1st × 4, 2nd × 3, 3rd × 3, 4th × 3, 5th × 2, 6th × 1, 7th × 1, and 8th × 1.  So, for those 19 Spells Known, you can choose any spells from 1st through 8th spell level. Am I free then to select as many spells as I can at 8th spell level (5 in number), working backwards, and in the end ignoring the 1st, 2nd, 3rd level spells entirely?  As another example, the Ranger doesn't know any spells at 1st level, nor have any spell slots, but the book says “You know two 1st-level spells of your choice from the ranger spell list.” Does it mean at 2nd level and above?  Long story short: When choosing Spells Known for a spellcasting character created above 1st level, am I allowed to choose my Spells Known at whatever spell level I like, just so long as I have at least one spell slot of that level?  I'm working on a D&amp;D 5e character generator and need to clarify this. Question: If $c\neq 1$ is an $n^{th}$ root of unity then, $1+c+...+c^{n-1} = 0$  Attempt: So I have established that I need to show that $$\sum^{n-1}_{k=0} e^{\frac{i2k\pi}{n}}=\frac{1-e^{\frac{ik2\pi}{n}}}{1-e^{\frac{i2\pi}{n}}} =0$$ by use of the sum of geometric series'. My issue is proceeding further to show that this is indeed true. Do lure modules and incense cause new pokemon to spawn near you, or existing pokemon to be drawn to you?