According to :     The  is the most controversial axiom in the entire history of mathematics. Yet it remains a crucial assumption not only in set theory but equally in modern algebra, analysis, mathematical logic, and topology (often under the name Zorn's Lemma).   I am not a set theorist, and I don't pretend to be, but I have heard of some weird things that can happen with choice, such as the --paradoxes like these are presumably why the Axiom of Choice was so controversial at first, but I am interested in what would happen without choice.     Question: What notable consequences would occur without the Axiom of Choice?   I found one very interesting example  on an MO thread (reproduced here for ease):     The universe can be very a strange place without choice. One consequence of the Axiom of Choice is that when you partition a set into disjoint nonempty parts, then the number of parts does not exceed the number of elements of the set being partitioned. This can fail without the Axiom of Choice. In fact, if all sets of reals are Lebesgue measurable, then it is possible to partition $2^{\omega}$ into more than $2^{\omega}$ many pairwise disjoint nonempty sets!   What other weird things would result without this axiom? Would it really be a devastating blow to mathematics or is it really not that big of a deal? I'm hoping for examples/answers geared toward the undergrad level--suitable for someone with very little set theory background.
What is the advantage of accepting the axiom of choice over other axioms (for e.g. axiom of determinacy)?  It seems that there is no clear reason to prefer over other axioms..  Thanks for help.
How to check if Node connected to another node input in Python I am doing a process to some switch links in materials. I need to know if something is ever linked or not before to process. I can't find out how to :/ The script works well if something is linked only.  import bpy for m in bpy.context.object.material_slots:     mat = m.material     nodes = mat.node_tree.nodes      # get node input (socket)     alphasocket = mat.node_tree.nodes.get("Principled BSDF").inputs[18]     # get node link that connects into the socket     lnk = (link.from_socket for link in mat.node_tree.links if link.to_socket == alphasocket)      #add emission node     emi= nodes.new('ShaderNodeEmission')     emi.name= "emibak"     outepute= mat.node_tree.nodes.get("Material Output").inputs[0]      #make new link destination     #here 's where I cant find out how to check     if lnk != None:         print(mat.name + " alphanod found")        # mat.node_tree.links.new(lnk, emi.inputs[0])     else :         print(mat.name + " alphanod missing")      mat.node_tree.links.new(emi.outputs[0], outepute)     here is another way I am searching...  import bpy  for m in bpy.context.object.material_slots:      mat = m.material     nodes = mat.node_tree.nodes          print("**** Material " + mat.name+ " ****")      for mat_node in mat.node_tree.nodes:         if mat_node.type == 'BSDF_PRINCIPLED':             print("From " + mat_node.name )                         alphasocket = mat_node.inputs[18]             #print(alphasocket)             node_in = mat_node.inputs             #print(node_in)                    for n in alphasocket.links:                                print("Alpha connected to " + n.from_node.name)   This show me what is connected to the alpha channel but if nothing is connected I want to connect a new node. Fast way to copy a large file on a LAN I am having some trouble with NFS, and I'd like to try using just plain old TCP.  I have no idea where to begin, though.  Hardware-wise, I am using an ethernet crossover cable to network two netbooks.  To network them, I type  $ sudo ifconfig eth0 192.168.1.1 up &amp;&amp; ping -c 10 -s 10 192.168.1.2 &amp;&amp; sudo /etc/init.d/nfs-kernel-server start   on the first netbook and  $ sudo ifconfig eth0 192.168.1.2 up $ ping -c 10 -s 10 192.168.1.1 $ mount /mnt/network1   on the second  where /mnt/network1 is specified in /etc/fstab as  192.168.1.1:/home /mnt/network1 nfs noauto,user,exec,soft,nfsvers=2 0 0  as well as in /etc/exports (using the syntax of that file), on the first netbook.  The above works fine, but the files and directories are huge. The files average about half a gigabyte a piece, and the directories are all between 15 and 50 gigabytes.   I'm using rsync to transfer them, and the command (on 192.168.1.2) is  $ rsync -avxS /mnt/network1 ~/somedir   I'm not sure if there's a way to tweak my NFS settings to handle huge files better, but I'd like to see if running an rsync daemon over plain old TCP works better than rsync over NFS.  So, to reiterate, how do I set up a similar network with TCP?  UPDATE:  So, after a good at few hours of attempting to pull myself out of the morass of my own ignorance (or, as I like to think of it, to pull myself up by my own bootstraps) I came up with some useful facts.  But first of all, what led me on this rabbit trail instead of simply accepting the current best answer was this: nc is an unbelievably cool program that resolutely fails to work for me. I've tried the netcat-openbsd and netcat-traditional packages with no luck whatsoever.  The error I get on the receiving machine (192.168.1.2) is:  me@netbook:~$ nc -q 1 -l -p 32934 | tar xv Can't grab 0.0.0.0:32934 with bind tar: This does not look like a tar archive tar: Exiting with failure status due to previous errors   route gives:  me@netbook:~$ route Kernel IP routing table Destination     Gateway         Genmask         Flags Metric Ref    Use Iface default         dir-615         0.0.0.0         UG    0      0        0 wlan0 link-local      *               255.255.0.0     U     1000   0        0 eth0 192.168.0.0     *               255.255.255.0   U     2      0        0 wlan0 192.168.1.0     *               255.255.255.0   U     0      0        0 eth0   But, here's the good news: having the static IP addresses set in /etc/network/interfaces, which I started doing while trying to get nc working, fixed all my NFS problems and rekindled my love for NFS.  The exact configuration I used (with 192.168.1.1 for the first netbook, of course) was:  auto eth0 iface eth0 inet static address 192.168.1.2 netmask 255.255.255.0   With those settings, the two netbooks will be able to ping each other directly after being booted up, without even an ifup.  Anyway, I'd still really like to see nc in action, so I'm hoping someone help me debug this process. I'm using Drupal seven. I want to make the options in a select list be dependent on the value chosen in another select list in a form.  I'm sure this has been asked many times before, but I am having difficulty finding a clear answer for how to do this.  The form is for users to enter a work history.  They need to select a squadron which is a node reference to the squadron field type, and this is in a drop-down list.  However, the squadron, is dependent upon a city drop-down list.  Users first need to select a city which will then filter the options for the squadron.  In the squadron content type, I created a taxonomy for city which gets tagged to the squadron.  I would be very grateful for any pointers as to the best way (simplest?) to go about this, or for any useful resources online which would help. I read a YA novel in the early 2000s that I think takes place on Earth some time in the future. The human race has been enslaved by some other race, possibly aliens. If I remember correctly, humans were kept as slaves for some purpose and then exterminated at age 16, and I think some girls were kept to breed.  I remember scenes of a band of teenagers walking around sewers fighting these aliens who bled a blue "ichor." The only thing I distinctly remember about the book was that it was the first place I saw the word "ichor."  This is a pretty sorry description; but does anyone have a clue what this book was? Exact Duplicate:        I was reading an article on MSDN where I found a mention to google-fu. It says, “To search for C++ delimeters and code snippets is going to take a little Google-fu on the reader's part.” what does google-fu mean? Finding a permutation, and number of, from powers of the permutation Can we start cleaning up [table] tag and burninate it ASAP Related questions:     (This led to founding of )   The tag  has become cluttered with all kinds of questions ranging from sql tables (for all DBM systems, HTML tag &lt;table&gt;, outputting content in any language (PHP, C#, LaTeX to name a few) as a table and several plugins of various languages and/or IDEs (like jTable, tablesorters and the kind).  The current count stands at 18,315 questions having this ambiguous tag. A few of possible suggestions for cleaning process:    +  to  |   +  to  |   +  to  |   +  to  |   + other-specific-DBM systems to whatever_DBM_it_is-table  +  to  |    Since I've no idea about other languages and their specific features regarding table, I'd ask the community for their input on this (such as , ,  and ). The other questions are either tagged with arrays or sql and similar tags, and in my opinion, just removing  from such questions would be enough! iOS 12 tapping on notification to open app not working Convert .mov to .mp4 I want to convert .mov to .mp4! I saved the video from iMovie but it is in .mov format! How do I convert it to .mp4?  I'm using a MacBook and I want to share it to my phone, but my phone can't open .mov format video. Let $f:\mathbb{R}\to\mathbb{R}$, $f(kx)=f(x)$. Show that if $f$ is continuous at $0$ then $f$ is a Constant function Let $f:\mathbb{R}\to\mathbb{R}$ , there is $k \in \mathbb{R}$, $|k|\ne 1$, so that for every $x\in \mathbb{R} , f(kx)=f(x).$ Show that if $f$ continuous at $0$ then $f$ is a constant function.   I tried to find something to show it from the definition of continuous function but I didn't know how to continue. We have that $f$ continuous at $0$ if for every $\epsilon&gt;0$ there is $\delta&gt;0$ such that $|x-0|&lt;\delta \implies |f(x)-f(0)|&lt;\epsilon$ And if $f$ not continuous on $0$ is $f$ still a constant function? SSH: How to disable weak ciphers? Security team of my organization told us to disable weak ciphers due to they issue weak keys.    arcfour   arcfour128   arcfour256   But I tried looking for these ciphers in ssh_config and sshd_config file but found them commented.   grep arcfour * ssh_config:#   Ciphers aes128-ctr,aes192-ctr,aes256-ctr,arcfour256,arcfour128,aes128-cbc,3des-cbc   Where else I should check to disable these ciphers from SSH? Retaining all fishnet grid squares within boundary of polygon from another feature class? I have created a fishnet grid (3km x 3km) over a vector polygon.   I now want to clip the fishnet over the vector polygon retaining all grid squares within the boundary of the polygon.   Therefore I want all squares that would typically be clipped into partial squares to remain as whole squares.   Does anybody know how to do this? Regular expression for URL How to select faces by area I found this documentation:   Under "Face Selection Mode" it says:     Face Selection Mode:      ...        Area   Selects all faces that have a similar area as those already selected.   But I can't figure out where in blender this option is hiding? I am new to the amsart document class. For some reasons \author (etc..) is not showing after I use \maketitle. This is my tex:  \documentclass[12pt,reqno,a4paper]{amsart}  \usepackage{amsmath} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{mathrsfs}  \usepackage{amsthm}  \usepackage{latexsym}  \usepackage{pictexwd} \usepackage{pdftricks} \usepackage{natbib} \usepackage{setspace} \usepackage{color} \usepackage[affil-it]{authblk}  \begin{document}  \title{Temptation, Asymmetric information and Committment}  \author{Mark}  \affil{University of Leicester}  \date{February 2014}  \maketitle  \begin{abstract} To be written \end{abstract}  \section{introduction}  ...  \end{document}   and this is the output:   can anybody help me out? Can one attack for damage after having grappled an opponent? The grappling rules sure are... light. Supposing one has an Extra Attack:   Assuming one has successfully grappled an opponent with one's first attack, can one then perform a normal attack action with one's Extra Attack? Against the grappled opponent or any opponent within reach? Limitations on weapons (e.g. one-handed only)? Assuming one has successfully grappled an opponent with one's first attack, can one's grappled opponent (now with move 0) perform a normal attack action? Against you or against any one in reach? Do advantage and disadvantage (along the lines of restraint) come into play? Are there grappling-specific attacks for damage (e.g. choke-hold)? How to show that the nth power of a $n \times n$ nilpotent matrix equals to zero $A^n=0$ $A$ is a $n\times n$ matrix such that $ A^m = 0 $ for some positive integer $m$.   Show that $A^n = 0$.   My attempt: For $n &gt; m$, it's obvious since matrix multiplication is associative.  For $n &lt; m$, $A^n\times A^{m-n} = 0$; not sure what to do next. Also I know that $\det A = 0$. How to turn off magic quotes on shared hosting? I want to turn off PHP's magic quotes.  I don't have access to php.ini.  When I tried to add php_flag magic_quotes_gpc off to my .htaccess file, I get a 500 internal server error. This is what my .htaccess file looks like:  AddType x-mapp-php5 .php php_flag magic_quotes_gpc off   Then I tried to use ini_set('magic_quotes_gpc', 'O'), but that had no effect.  How do I turn magic quotes off? Vectorization operator Is there any bidirectional 5v-3.3v level shifter? Is there any IC that interfaces any 3.3V Input/Output to 5V Output/Input? I need it primarily for an Arduino Due but if there any bidirectional IC that works like that it would be great.  Some people advised me to use the SN74AHC125 and CD4050 ICs, but I don't understand how they work or how to interface with them.