Are $\mathbb{Q}$ and $\mathbb{Z}$ homeomorphic?
Proving $\mathbb{Q}$ isn't homeomorphic to $\mathbb{Z}$
Dealing with suggested edits on question to be closed as duplicate What is the difference between \em and \emph? What is the difference between \emph{...} and {\em ...}?  When to use each of them? VHDL Transition Function Install java Runtime Environment Here is the problem: From any IP address not belonging to your mail server:  telnet me.myemailserver.com 25    helo me.someserver.com mail from: &lt;yourusername@mydomain.com&gt; rcpt to: &lt;yourusername@mydomain.com&gt; data This is spam.  Buy my stuff. .   I'm using Postfix.  I'm having a problem finding a solution to requiring SMTP-AUTH for email claiming to be from mydomain.com.  Googling around, this guy has identified the same problem (where I cut-n-paste with some modifications) the above example from:   This link   gets close to a solution but it has a side effect of requiring SMTP-AUTH for mail not from mydomain.com.  For mail not claiming to be from mydomain.com, I would do the usual RBL and Spam filtering.  In short, I want to reject mail to local domains (mydomain.com) from outside/unauthenticated clients claiming to be from local domains (mydomain.com).  This is what I tried: I've tried both permit and reject as the default.  Here is exact excerpt from my main.cf:  smtpd_recipient_restrictions = reject_unauth_pipelining,                            permit_sasl_authenticated,                            check_recipient_access pgsql:/etc/postfix/pgsql-recipient.cf,                            reject_unauthenticated_sender_login_mismatch,                            reject_unauth_destination,                            reject_unlisted_recipient,                            check_sender_access pgsql:/etc/postfix/pgsql-sender.cf,                            reject_unlisted_sender,                            reject_invalid_hostname,                            reject_non_fqdn_hostname,                            reject_non_fqdn_sender,                            reject_non_fqdn_recipient,                            reject_unknown_sender_domain,                            reject_unknown_recipient_domain,                            reject_rbl_client cbl.abuseat.org,                            reject_rbl_client sbl.spamhaus.org,                            reject_rbl_client sbl-xbl.spamhaus.org,                            reject_rbl_client bl.spamcop.net,                            reject_rbl_client dnsbl.njabl.org,                            reject_rbl_client blackholes.wirehub.net,                            reject_rbl_client relays.mail-abuse.org,                            reject_rbl_client dialups.mail-abuse.org,                            reject_rbl_client blackholes.mail-abuse.org,                            reject_rhsbl_sender dsn.rfc-ignorant.org,                            (reject and permit both tried here) I wonder about the Adjustments to Cost Basis after a wash sale occur. Considering this  ( from marketwatch.com) where someone: On 1 Dec, 2018 used an amount of money in his account to buy 100 shares of XYZ Co., for $2000 (to make it simple , let's say 1 Feb, 2019 to turn all the transactions into the same year) On 1 Apr, 2019 he sells the shares for $1200, and incurred a loss of 800$. On 10 Apr, 2019 he bought back 100 shares for $1300, and had a wash sale. The 800$ loss gets added to the cost basis of this transaction( and the basis becomes $2100) Now, If on 13 Apr 2019, he sold 100 shares for $1400; I'm pretty sure that the realized Gain/Loss record of this transaction would show something like this: &quot; XYZ Co. shares  100 , Proceeds $1400 , Cost basis  $2100(adjusted), Short-term Gain/Loss  -$700 &quot;. So, even though the Gain/Loss shows a negative number, he still got an actual profit of $100 from this sale, right? How to format hard disk in Ubuntu 14.04? What Is the Real Name of the #? I made a huge project, wanted to reduce file size from 1.3GB to below 1GB. Compressing did not help. I removed objects from scene. Also textures. I then realized, the file size even was the same when I delete ALL objects. Why?  Download of sample:   Before deleting all: 1.2GB, after: 1.1GB. What bizarrities lurk within the decimal expansion of an irrational number? i.e. can we write  $\pi = 3.14159\dots X\dots$  where $X$ consists of (say) $10^{100}$ consecutive zeroes?  [Originally asked on reddit without response :-( ] Okay I have the following fitch proof almost figured out, from here I know I have to move forth in conlcuding but I don't know what I am missing  (2 premises)  S → (R ∨ P)  P → (¬R → Q)   my work below  new scope assume S   Rule: > elim  R ∨ P  New scope assume R  Q∨R     Rule: V intro  End scope – (new scope assume P)  ¬R → Q         Rule: > Elim  my confusion comes where I go from here  Q∨R            rule Taut Con ??  Goal:├ S → (Q ∨ R) If we remove the square in the upper right corner of a $8\times 8$ chessboard.  The question is: Is it possible to cover the entire remaining area, with $1\times 3$ chocolate bars? (they can be laid on the chessboard vertically and horizontally aswell)  For the answer: We know that there will be $63$ squares left on the chessboard, of which $32$ are white and $31$ are black, since the one in the upper right corner was black. $63$ is divisible by $3$, so it could be possible to cover the area, but that doesn't prove that an arrangement exists to do it. I'm not sure how to continue and am seeking help. Thanks. Prove that a limit doesn't exist In my assignment I have to prove that the following function doesn't have a limit:  $$f(x)=\frac{x}{x-\lfloor{\sin x}\rfloor}$$ when $${x \to 0}$$  In other words, I have to prove that for every $\delta$ such that $0&lt;|x-{x_0}|&lt;\delta,$ $|f(x)-L|&gt;\epsilon$.  In fact, I don't even know how to start. Do I choose my $\delta$? I know that the sin function has certain values that's supposed to help me. How do I use it?  I have to prove this by definition, so I can't use limit arithmetic for example  Thanks. Anyone seen this one yet? Vote too old to be changed, unless post is edited My vote was only a few hours old. Then I realized the answer was wrong. Updated my question and went to remove the vote. Even after updating question I still have the issue. Small issue, but frustrating.  See also: I have two different machines (home and work) running Ubuntu 18.04. Last night vim froze at home. I was in insert mode and typing and went to save (esc :w) and nothing happened. The status bar still reads -- INSERT --, the cursor is still blinking where it was. I was stuck. I couldn't find a way out. I couldn't type (nothing happened when I type), I couldn't move around (the up and down arrows did nothing). It was stuck in insert mode with the cursor blinking where it was.   I was definitely multitasking and probably hit some other keys in there, but I don't know what keys. It was late, though, so I closed the terminal window and tried again (I was entering a git commit message). It happened again partway through my typing so I switched to git commit -m "don't need an editor for this" instead. And then I shut down my computer and stopped working.  I figured I was just tired, but then it happened to me today at work on a different laptop altogether. Again I was multitasking and can't swear I didn't type any bizarro key sequence but if I did it was accidental. And other tabs in the same terminal aren't frozen.   I'm used to getting trapped in visual mode in vim. That's a trick I've learned. But stuck in insert mode? Any ideas on what I might've done and how to get out of it?   Per a comment suggestion I tried looking at .viminfo but the only .viminfo I see is owned exclusively by root and only appears to show things I would have edited with sudo:   # Input Line History (newest to oldest):  # Debug Line History (newest to oldest):  # Registers:  # File marks: '0  1  0  /etc/neomuttrc |4,48,1,0,1531789956,"/etc/neomuttrc" '1  1  66  /etc/apt/sources.list.d/signal-bionic.list |4,49,1,66,1530816565,"/etc/apt/sources.list.d/signal-bionic.list" '2  51  0  /etc/apt/sources.list |4,50,51,0,1530816531,"/etc/apt/sources.list"  # Jumplist (newest first): -'  1  0  /etc/neomuttrc |4,39,1,0,1531789956,"/etc/neomuttrc" -'  1  66  /etc/apt/sources.list.d/signal-bionic.list |4,39,1,66,1530816565,"/etc/apt/sources.list.d/signal-bionic.list" -'  1  66  /etc/apt/sources.list.d/signal-bionic.list |4,39,1,66,1530816565,"/etc/apt/sources.list.d/signal-bionic.list" -'  51  0  /etc/apt/sources.list |4,39,51,0,1530816531,"/etc/apt/sources.list" -'  51  0  /etc/apt/sources.list |4,39,51,0,1530816531,"/etc/apt/sources.list" -'  51  0  /etc/apt/sources.list |4,39,51,0,1530816531,"/etc/apt/sources.list" -'  51  0  /etc/apt/sources.list |4,39,51,0,1530816531,"/etc/apt/sources.list" -'  1  0  /etc/apt/sources.list |4,39,1,0,1530816447,"/etc/apt/sources.list" -'  1  0  /etc/apt/sources.list |4,39,1,0,1530816447,"/etc/apt/sources.list" -'  1  0  /etc/apt/sources.list |4,39,1,0,1530816447,"/etc/apt/sources.list" -'  1  0  /etc/apt/sources.list |4,39,1,0,1530816447,"/etc/apt/sources.list"  # History of marks within files (newest to oldest):  &gt; /etc/neomuttrc     *   1531789952  0     "   1   0  &gt; /etc/apt/sources.list.d/signal-bionic.list     *   1530816564  0     "   1   66     ^   1   67     .   1   66     +   1   66  &gt; /etc/apt/sources.list     *   1530816454  0     "   51  0   It seems odd that I wouldn't have an unprivileged .viminfo but I did sudo udpatedb and locate .viminfo and still didn't surface more than the one root-owned file. Let $A,B$ be any two sets. I really think that the statement $|A|\leq|B|$ or $|B|\leq|A|$ is true. Formally:     $$\forall A\forall B[\,|A|\leq|B| \lor\ |B|\leq|A|\,]$$   If this statement is true, what is the proof ? Under , is $\exists x(x=a)$ true in every interpretation in first order logic (FOL) with equality? If so, could $\exists x(x=a)$ be considered a tautology? This question was motivated by  which was closed for lacking clarity. Here I have attempted to add that clarity myself so that the same question can be useful to others who are wondering a similar thing. This is a self answer question. Why does Venus spin in the opposite direction? Given: Law of Conservation of Angular Momentum.   Reverse spinning with dense atmosphere (92 times > Earth &amp; CO2 dominant sulphur based). Surface same degree of aging all over. Hypothetical large impact is not a sufficient answer.   Assuming any object large enough to alter a planets rotation or even orbit would likely destroy most of its shape, yet Venus has retained a spherical property with a seemingly flat, even terrain indicating no volcanoes,and few if any visible meteor impacts. It would be fragmented and dispersed for billions of years.  Even the question of what meteor, comet, asteroid composition could survive traveling that close to the sun's temperature, radiation, electromagnetic energy, solar flares, or gravity to equal a mass reactionary change as to alter it's spin. How should I apply brick to an interior wall? For QA workstations preparation (Windows-based PCs) our IT department uses typical batch deployment tools. I'm not at all interested in the details of such process, but IT guys ask me:  What typical set of software you need for everyday manual testing tasks? We could include these in our deployment so that you guys could save more time for testing, not for environment prep &amp; tuning.  Sure thing we do test various range of projects, from web applications to standalone solutions, and each application requires its own set of tools for manual testing, e.g.:  Browsers Virtualization utilities DB clients Screens capturing tools FTP clients XML editors etc.  However, and that's for sure - there's a list of tools every QA MUST have installed on its PC, regardless of project types under testing. My area of experience is mostly standalone / complex web apps, that's why my vision on the task is a bit subjective. So, your suggestions of what are tools / software an average QA specialist can't live without will be highly appreciated. 2 assumptions:  Manual testing is a point of interest. Let's limit the list to not more than 15 (better 10) items.  Thanks in advance!