Space-time infinite
Did spacetime start with the Big bang?
How do I add PHP code/file to HTML(.html) files? Prove by induction that $n! > 2^n$ Suppose that when $n=k$  $(k\geq4)$, we have that $k!&gt;2^k$.  Now, we have to prove that $(k+1)!\geq2^{k+1}$ when $n=(k+1)$ $(k\geq4)$.  $$(k+1)! = (k+1)k! &gt; (k+1)2^k  \text{ (since }k!&gt;2^k)$$  That implies $(k+1)!&gt;2^k2$, since $(k+1)&gt;2$ because of $k$ is greater than or equal to 4.  Therefore $(k+1)!&gt;2^{k+1}$  Finally  we may conclude that $n!&gt;2^n$ for all integers $n\geq4$    Solved, thank you! How to Edit PDFs? Can i install ubuntu on meizu mx4 android edition like ubuntu edition with iso recovery in this page "  " Let $g(x)\in \mathbb{Z}[x]$, a nonconstant polynomial. Show that the set of primes $p$ such that $p\mid g(n)$ for some $n\in \mathbb{Z}$ is infinite.  I don't know how to start. I have tried asuming that the set is finite but i haven't reached any contradiction. I am new to TeX/LaTeX. How do I install TeX on Windows (7)? It seems that there are many different implementations, so which one is best for my OS? What books are recommended for an advanced undergraduate course in electrodynamics? I've played around in the past of the 2D Flash fan-made version of the popular Valve game Portal.  It has basically the exact same mechanics, but as a 2D side-view flash game.  Lately I've toyed around with creating a simplified flash version of some of my favorite franchises (such as Zelda, Mario, Splinter Cell, etc.).  Of course, nothing is "stopping" me from just using the same mechanics and just changing the name to something not copyrighted.  I have witnessed projects that have tried to directly port a 3D game into a 2D simplified version, with the exact same plot and puzzles (Ocarina of Time in 2D comes to mind), and I have seen them being shut down.  But I am not likely going to exactly duplicate any game...just borrow some of the source material and basic underlying mechanics.  For example, if I were to make a Zelda-influenced fan game, I would have items such as the Hookshot, Boomerang, and all other sorts of ones from the Gameboy Zeldas; just with a custom plot and dungeons.  With likely the same mechanics.  What are the legal issues involved in this?  I used to think it was a "Don't do this ever; it's a bad idea."  But then I've seen the Portal clone, and now I'm curious. Retrieving Data from remote database As of the November 2018 core book updates, what changes were made in the latest printings of the PHB that aren't noted in the errata document? I want to install OpenOffice. What can I do to install it on my computer? Possible Duplicate:          I have tried using \text{\~{}} to draw a tilde in math mode. However, this only produces a superscript tilde.  I have looked around at many pages such as this one:   and surprisingly, I can't find where to draw a tilde in math mode (not under or above a character - just a single tilde character). If I just use ~, then nothing appears. How will people upgrade from 12.10 to later releases after 13.04 is EOL? RX 590 IN Blender and Cycles Render I don't know why, but I cant render anything in CUDA and OptiX but OpenCL work fine. I cant use Cycles render because it's very laggy. I have newest  version of Blender and an RX 590 Red Dragon 8gb. Why does that happen?  How can I turn on my gpu? e.g., I've got files I want to send by sendmail but the receiving mailbox (for posting pictures to my blog) will not accept uuencode files a la   $uuencode file | sendmail user@domain  I'm guessing it'll accept MIME though. So what command can I use instead? The  says that there is a moderator election occurring.   How does the election work and how can I get involved? How do I SSH to machine A via B in one command? I need to graph a rectangle on the Cartesian coordinate system. Is there an equation for a rectangle? I can't find it anywhere. I just installed ubuntu 11.10 from a usb stick.   After installation, none of the software which I had collected and run on 11.10 or 11.04 runs on it. Even my newly downloaded opera or chrome installations does not work.  I do not have a internet connection.  Whenever i try to install any .deb file by double clicking it,software center opens up but the install button is grayed out. Always return data from last week's Monday thru Sunday