I have the following task:     Give an example of two $\sigma$-algebras such that their intersection is not an algebra   There is a hint that such situation is possible only when their units differ, but I still can't come up to solution.   Let $S_1,S_2$ be our $\sigma$-algebras and $X = S_1 \cap S_2$.  1) $A,B \in X \Rightarrow A \setminus B \in X$. This is obvious because $A,B \in S_i \Rightarrow A \setminus B \in S_i$ (for $i=1,2$).  2) Similarly, $A,B \in X \Rightarrow A \cup B \in X$.  3) Similarly, any countable union is in $X$ too (though we do not need $X$ be a $\sigma$-ring by condition of the task).  So $X$ is at least a $\sigma$-ring and it must not contain a unit (or otherwise it will become an algebra).  If $X$ is countable, then union of all its elements $A = \bigcup A_i$ is contained in $X$. This easily makes $A$ a unit. Thus our $X$ must be uncountable. And from here I can neither prove that $X$ contains a unit nor disapprove it.
I have the following question:    $\textbf{Question}:$ Let $\mathcal{F}_1$ and $\mathcal{F}_2$ be two algebras. Is $\mathcal{F}_1 \cap \mathcal{F}_2$ a $\sigma$-algebra?  I believe the answer is no. I know the definition of an algebra and the definition of $\sigma$-algebra.    I'm assuming I need to show that the intersection of the finite unions of each algebra is finite, but then I get stuck trying to work out how to show it is not a $\sigma$-algebra.  All help is appreciated.  Many thanks, John
I'm a Windows/Mac/Ubuntu and Android user, so I know what I'm talking about, when I say: How do I open binary image files? (.img) They just won't open, on any OS…  I'm an Android dev… I'm currently working on a ROM, (I also program, using Windows) but I need to extract files, from .img files. I've converted them to .ext4.img but they just aren't recognized by Linux (Definitly not by Android), by Mac OS or Windows. In other words, I can't open, extract or mount them.  Can anyone help me? I'm kinda confused… What is the best way to remove accents (normalize) in a Python unicode string? What will be the trajectory of the given motion If it is given that component of acceleration perpendicular to the velocity of a body has a constant, non-zero magnitude, how can we mathematically prove that the trajectory of the body will be circular?   I have basic knowledge of calculus, vectors and co-ordinate geometry. I can prove that the trajectory of a body in projectile motion is parabolic. I tried to follow a similar method to get an equation of circle but couldn't succeed. I tried forming parametric equations of x and y in terms of time t (the way we proceed when proving the parabolic path of a projectile) but could not reach the conclusion.  Edit: I have edited the question in order to improve it. However I still can not share my work on this question as I had asked the question almost 6 months ago and now I can not find where I tried solving it. Sincerely sorry for that. ¿Can you help me with axiom of regularity? I understand that if we define a set such that $A=\{A\}$ we have then a contradiction because of regularity axiom, thus, a set can not be a member of itself. My question is; how can it be so, if I define a set $A=\{A,b\}$ ($b$ disjoint from $A$)?  Thanks. What's the best way to get the last N elements of a Perl array? When I used  pip install ipython   or  pip install "ipython[notebook]"   I get the following error:  Downloading/unpacking ipython   Downloading ipython-2.3.1-py27-none-any.whl (2.8MB): 2.8MB downloaded Installing collected packages: ipython Cleaning up... Exception: Traceback (most recent call last):   File "/usr/lib/python2.7/dist-packages/pip/basecommand.py", line 122, in main     status = self.run(options, args)   File "/usr/lib/python2.7/dist-packages/pip/commands/install.py", line 283, in run     requirement_set.install(install_options, global_options, root=options.root_path)   File "/usr/lib/python2.7/dist-packages/pip/req.py", line 1435, in install     requirement.install(install_options, global_options, *args, **kwargs)   File "/usr/lib/python2.7/dist-packages/pip/req.py", line 671, in install     self.move_wheel_files(self.source_dir, root=root)   File "/usr/lib/python2.7/dist-packages/pip/req.py", line 901, in move_wheel_files     pycompile=self.pycompile,   File "/usr/lib/python2.7/dist-packages/pip/wheel.py", line 206, in move_wheel_files     clobber(source, lib_dir, True)   File "/usr/lib/python2.7/dist-packages/pip/wheel.py", line 193, in clobber     os.makedirs(destsubdir)   File "/usr/lib/python2.7/os.py", line 157, in makedirs     mkdir(name, mode) OSError: [Errno 13] Permission denied: '/usr/local/lib/python2.7/dist-packages/IPython'  Storing debug log for failure in /home/username/.pip/pip.log   What does this error mean? How do I fix it? I was wondering how to add plugins to my Minecraft server. I am using Bukkit, and the things I would like to be able to do is spawn stuff, teleport to other players, set home locations, have an in-game currency/shop and be able to teleport to homes. Shell Script for logging into a ssh server I tried writing a shell script which can do automatic login into a ssh server using password which is mentioned in the script. I have written the following code:  set timeout 30 /usr/bin/ssh -p 8484 root@172.31.72.103 expect  {    "root@172.31.72.103's password"     {       send "password\r"     } }   This code is not running properly, still it is asking for the password. Can somebody please help me in solving this Process Builder - Breaking Production Deployments? I have a Process Builder flow set up and I am running some tests around the InvocableMethod Apex code. The tests pass fine in my staging and production environments. Yet, when I try to deploy to production, I get a strange error.  CANNOT_EXECUTE_FLOW_TRIGGER, The record couldn’t be saved because it failed to trigger a flow.  Thankfully I received a somewhat more informative error email.  UPSERT FAILED ---  ERRORS :  (CANNOT_EXECUTE_FLOW_TRIGGER) The record couldn’t be saved because it failed to trigger a flow. common.exception.AssertionException: ORA-20070: Cannot read from apex_class and apex_trigger while running tests ---  for SFDC record with ID : null,  Unfortunately, the deployment has nothing to do with the flow and it is unclear why it is failing. What is the root cause of this error and how can I fix it? EDIT: I found out this is a . The other claimed workaround is to deploy via the Metadata API. UPDATE: Because I was subscribed to the Known Issue, I received the following confirmation this issue is resolved.  We are pleased to notify you that the following Known Issue has been resolved: Executing an InvocableMethod during an apex test run from a change set can cause Errors. Thank you for being patient while we worked to address this issue. Please feel free to reach out to Customer Support if you have further questions. Sincerely, Salesforce Success Team Protect .NET code from reverse engineering? In computer science we discuss an abstract machine called a "deterministic finite automaton". The standard initialism for this term is "DFA". This makes sense in the singular usage of the initialism.  However, the pluralization of the word "automaton" is "automata". One speaks of "an automaton" or "many automata". Consequently, it seems intuitive to form an initialism of the phrase "deterministic finite automata" as "DFA".   This does not seem correct, as "DFA" could be either plural or singular. On the other hand, "DFAs" also does not seem correct because it would seem to expand to "deterministic finite automatons", a phrase which no self-respecting computer scientist would ever utter.   This appears to be a duplicate of the question here   But that question was never clearly resolved. What to do? Deriving ordered statistics minimum cdf Assume ${{X}_{1}}$, ${{X}_{2}}$, ${{X}_{3}}$,...,${{X}_{n}}$  are i.i.d. samples from distribution with density f, and cdf F.  Let V=min( ${{X}_{1}}$, ${{X}_{2}}$, ${{X}_{3}}$,...,${{X}_{n}}$)  To find the minimum $${B}_{v}={\{V\ge{v}\}}=\{{X}_{1}\ge{v}\}\cap\{{X}_{2}\ge{v}\}\cap...\cap\{{X}_{n}\ge{v}\}$$  So, $$P(V\ge{v})=[1-F(v)]^{n}$$  The cdf is  $$F_{v}(V)=1-[1-F(v)]^{n}$$   The density is $${f}_{v}(V)=\frac{d}{dv}[1-F(v)]^{n}=nf(v)[1-F(v)]^{n-1}$$   To find the density, why did we use $[1-F(v)]^{n}$ instead of $1-[1-F(v)]^{n}$, shouldn't we used the cdf to derive the pdf? How can I use text-processing tools to insert a new line after every N lines?  Example for N=2:  INPUT:   sadf asdf yxcv cxv eqrt asdf   OUTPUT:   sadf asdf  yxcv cxv  eqrt asdf Resize Move Partitions on Dual Boot System Is password confirmation necessary on a Change Password dialog? How to get a dock on multiple monitors I have two monitors, but only one dock, which is somewhat annoying, so my question is, how do I get multiple docks? (One on each screen) Site hosted on EC2 / Amazon held hostage with private key I have a new client whose previous developer has left her high &amp; dry with her site on Amazon/EC2. He holds the private key to the instance, and though she has full access to the Amazon control panel (she's paying $300/mo for a site that has like 3 visitors per week) she doesn't have any way to get her content off and move to a new host.  I'm not familiar with AWS and am not sure how to help her. The site's group/file permissions are screwed up on the server so exporting the content/database via her WordPress control panel isn't working.  Any ideas on how to help her? Thanks! Obviously, most beers are carbonated with carbon dioxide, while some stouts/porters are "carbonated" with nitrogen.  I was curious if there has been any notable experimentation with other gasses to "carbonate" beer. If nitrogen can introduce a "creamy" texture to a beer, I would think that other gasses would also be able to introduce their own characteristics on beer. If any of these experiments have done, what characteristics do these other gases impart?  I'm sure cost would be an issue for certain gasses that would prohibit its use in beer, but for purposes of this question, cost is irrelevant.  As an aside, what is the correct term to use, as opposed to "carbonate", for a question of this nature? Is there a way to adjust kerning for a specific character combination? Given a Java InputStream, how can I determine the current offset in the stream? I'd like something like a generic, re-usable getPosition() method that will tell me the number of bytes read from the starting point of the stream.  Ideally, I would prefer this to work with all InputStreams, so that I don't have to wrap each and every one of them as I get them from disparate sources.  Does such a beast exist?  If not, can anyone recommend an existing implementation of a counting InputStream?