Is it possible to prove that $x=\{x\}$ is false in ZF system?
¿Can you help me with axiom of regularity?
Proof of Equivalence Relation $R=\{(a,b)\in\Bbb N^2: 5\mid (2a+3b)\}$ Given a set of natural numbers ($\Bbb N$), and the relation $R=\{(a,b)\in\Bbb N^2: 5\mid (2a+3b)\}$. Is $R$ an equivalent relation?   My answer: Yes, because $2a + 3b$ is divisible by $5$, if and only if, $2a + 3b − 5b$ is divisible by $5$.  Is my reasoning right?   If it is not, then how do I prove that this is an equivalent relation? pure code formatting, to enhance a question, is impossible (without 2k rep) If an edit was suggested to an answer to my question and I go to this edit, I see the checkmark Loading OpenStreetMap data in QGIS? Find the sum $\sum_{n=1}^{\infty} \frac{\ln n}{n(n- \ln n)}$ Find the following sum : $\sum_{n=1}^{\infty} \frac{\ln n }{n(n- \ln n)}$  I couldn't find any way to solve.   I just want a hint, how to initiate? I am embedding a PDF file inside my LaTeX-generated PDF file using embedfile:  \usepackage{embedfile} \embedfile{myfile.pdf}   I would like to also insert a link that the user can click on to open the attachment.  Is there any way to do that? Getting computer's UTC offset in Python Where can I get a clean ISO of a specific build of Windows 10? Why didn't the Alliance send for Yoda instead of Obi-Wan? Setting environment variables on OS X What is the proper way to modify environment variables like PATH in OS&nbsp;X?  I've looked on Google a little bit and found three different files to edit:   /etc/paths ~/.profile ~/.tcshrc   I don't even have some of these files, and I'm pretty sure that .tcshrc is wrong, since OS&nbsp;X uses bash now. Where are these variables, especially PATH, defined?  I'm running  (Leopard). How do I change folder timestamps recursively to the newest file? What are the minimum root filesystem applications that are required to fully boot linux? How do I get from Terminal 1 to Terminal 5 in Fiumicino Airport? The official site mentions a shuttle bus service, I also googled but the infos are not clear, so I hope to find some firsthand experience.  I have a flight with a stop in Fiumicino, I will arrive in Terminal 1 and the next departure is from Terminal 5, the transfer time is around 5 hours.  Is it correct that I should go to Terminal 3 first (using the internal transfer area) and after exit from Terminal 3 and take the shuttle to Terminal 5?  The terminal 5 has a waiting area with some shops or is just a terminal for departure? In your opinion is better to wait some hours inside Terminal 3 before going out to take the shuttle bus? Magic 8 Ball Problem This problem is probably simple enough to have an analogous problem, I just don't know the name so I'm going to describe it and hopefully somebody can point me in the right direction.  The problem is this: estimating the number of sides of a .   Let's say you perform the following process:   Shake the "Magic 8 Ball" and mark down the result If the result has not previously been seen, add it to the set of possible results and label the trial "N" (for "new") If the result has been previously seen, label the trial "O" (for "old") Repeat all steps   I imagine the following kind of sequence occurring: NNNNONNOONOONOOONOOOONONNOONOOONNOONOOOOOONOOONOOOOOOONOOOOOOOONOOOOOOOO...  Now imagine we don't know there are twenty sides to a Magic 8 Ball. Or imagine that you have a Magic 8 Ball with 1000 sides. As the number of "new" trials approaches the actual number of sides, we'll get increasingly more "old" trials showing up in the mix. Once we've seen all of the possible results, we'll always get "old" results. But we're never 100% sure we've seen every single possible result.  So here are the questions I'm interested in:   As we proceed with trials, can we estimate the total number of "sides" of the Magic 8 ball based on the number of "new" and "old" trials up to this point? Can we calculate a probability that our current estimate is correct, or a probability that some bounded estimate is correct? executing web service using postman How to get bright concert photos? I've been starting to shoot some live music recently and have been doing an okay job and see an improvement with each time I shoot. However recently I was shooting and all of my photos have come out very dark, too dark to use really. I was shooting in manual with 1/100 shutter speed aperture as wide as possible and a 6400 iso. Any advice is welcome. Thanks in advance. Are there any versions of t-SNE for streaming data? My understanding of  and the Barnes-Hut approximation is that all data points are required so that all force interactions can be calculated at the same time and each point can be adjusted in the 2d (or lower dimensional) map.  Are there any versions of t-sne that can efficiently deal with streaming data? So if my observations are arriving one at a time, it will find the best location on the 2d map to place the new observation, or continuously update all points on the 2d map to account for ht new observation.  Would this even make sense or does it go against the setup of t-sne. How to label using just numbers from start of text field? In ArcMAP 10.2, I am trying to format the labels on my map.   If the label is   1402 Bowie Road  But  I want only to display numbers:  1402   What is the expression to create this? How can you convert a byte array to a hexadecimal string, and vice versa? How do I write a correct micro-benchmark in Java? How do you write (and run) a correct micro-benchmark in Java?  I'm looking for some code samples and comments illustrating various things to think about.  Example: Should the benchmark measure time/iteration or iterations/time, and why?  Related: