What is the fastest way to get a shallow copy the data of an object?
What is the most efficient way to deep clone an object in JavaScript?
Replace symbols with values without evaluation Is "connected, simply connected" Redundant? Here are my definitions of &quot;connected&quot; and &quot;simply connected.&quot;  A topological space $X$ is connected if and only if it is not the union of two nonempty disjoint open sets. A topological space $X$ is simply connected if and only if it is path-connected and has trivial fundamental group (i.e. $\pi_1(X)\simeq\{\mathrm{e}\}$ and $|\pi_0(X)|=1$).  It is a classic and elementary exercise in topology to show that, if a space is path-connected, then it is connected. Thus, if a space is simply connected, then it is connected. Yet, despite this implication, I've read several cases where the words &quot;connected, simply connected&quot; appear together. For example, in Kobayashi and Nomizu's Foundations of Differential Geometry, Volume 1, page 252, the following is written: &quot;Let $M$ be a connected, simply connected analytic manifold with an analytic linear connection.&quot; In  and  (Links to Journal Storage, also known as JSTOR), they use &quot;connected, simply connected&quot; on their first page. The first of these takes it a step further, referring to &quot;closed, compact, connected, simply connected $4$-manifolds,&quot; where a closed manifold (unfortunate terminology) is defined as a compact manifold without boundary. My question is simple: Why use the words &quot;connected, simply connected&quot; when being simply connected implies connectedness? Thank you. Why does the Community user approve and reject edits? Why does the Community user sometimes approve or reject edits? How does a machine know if my edit is valid? What does it mean if my edit was rejected by Community?     See also: Proving $T$ and $U$ are equal if I know $(X,T)$ and $(X,U)$ are hausdorff and compact This question is from Wayne Patty Exercise 4.2  Let $T$ and $U$ are Topologies on set X. Suppose $ (X,T) $ and $(X,U)$ are compact Haurdsorff Spaces. Prove that $T=U$ or $T$ is not a subset of $U$ or $U$ is not a subset of T.  I thought of proving it by this way: Assuming that if $T$ is a subset of $U$ or $U$ is a subset of $ T$ then $T=U$ must be true. But I was unable to think on how to use compactness or hausdorff property and was unable to proceed. Well, also this question was asked before on this website. But I am unable to understand how the solution will work despite trying to understand it for a fair amount of time as it was just outlined. So, I am looking for a detailed solution. Why are "south" and "southern" pronounced with different vowels? I was wondering why we pronounce the vowels in the words south and southern. They seem to be very closely related to each other. Both refer to the same direction. South is a noun and Southern is an adjective, which I don't think caused them to have a different vowel. Oxford Dictionary shows that south is /saʊθ/ and southern is /ˈsʌð(ə)n/. In short, south has a long vowel and southern has short. Nullable type issue with ?: Conditional Operator Could someone explain why this works in C#.NET 2.0:      Nullable&lt;DateTime&gt; foo;     if (true)         foo = null;     else         foo = new DateTime(0);   ...but this doesn't:      Nullable&lt;DateTime&gt; foo;     foo = true ? null : new DateTime(0);   The latter form gives me an compile error "Type of conditional expression cannot be determined because there is no implicit conversion between '&lt;null&gt;' and 'System.DateTime'."  Not that I can't use the former, but the second style is more consistent with the rest of my code. What is this mark over the question When I open a site I see a mark over a question.See screen shot.  When I open the question mark is not remove.It still appear.    is this bug or? How do I change a user name in Windows 7? I want my prompt to display:   current (absolute) working directory, colored in green and in a NEW line, the dollar sign and an empty space.   I am using this line in .profile  export PS1='\e[0;32m$(pwd)\n\e[m$ '  So when in e.g. Desktop, my prompt looks like this:    However, sometimes when hitting the up arrow to re-run previous commands, at the start of the prompt a random char sequence appear that does not seem to go away unless I hit enter, e. g.    I have never hit a cd cd Desktop command. The weirdest part is that backspace won't even delete the first one of the two cd commands above!  Any suggestions? How do I add this extra partition to my installed Ubuntu system? I started installing Ubuntu by watching a video tutorial about doing a disk partition installation, for that, inside Windows' 7 own disk partitioning tool. After a defrag I cut 100GB that I pretended to use on my Ubuntu installation for a little try out, now, while installing, I never really chose where I wanted Ubuntu to be installed, so I guess it just made a partition by itself of the minimum that the installation tells you it needs.  How can I now give the other 92 GB I had left apart only for that task?  Here's what my partitions look like now.     Here's a df:    And here's the GParted tool un ubuntu: Are these plural or singular? I was surprised when I heard zero is plural, and even 1.00001 is plural.  Then, what about following numbers ?  (1) 1.00  which means the value measured  between 0.995-1.004, having possibility that it was exactly 1.  (2) 0.99999.....  which is mathematically equal to 1. Also, are others that are mathemattically equal to 1 than this, treated completely same as 1?  (3) -1  Is this singular? Or negative numbers are generally plural?  (4) i = square root of -1  I know it's weird to count things with imaginary numbers, nonetheless, if you were to count, which form, plural or singular, would you be to use?  That's it. Why is ++i considered an l-value, but i++ is not? Why is ++i is l-value and i++ not? If $\sum_{n=1}^{\infty} a_n^{2}$ converges, then so does $\sum_{n=1}^{\infty} \frac {a_n}{n}$ Replace Line Breaks in a String C# How can I replace Line Breaks within a string in C#? English version of Ubuntu with Italian keyboard I want to install Ubuntu in ENGLISH (UK) but I have an ITALIAN keyboard, which has a different layout to the English keyboard. How can I install Ubuntu in English but select an Italian layout for the keyboard. I tried, but it would only allow me to select an English keyboard. Thanks How to do binary calculation？ How do I handle elastic contacts in a simulation with friction I'm trying to simulate a wheel as it hits the ground.  Problem 1  Suppose a disc is dropped from a height. It has initial velocity of $-x,-y$ caused by throwing and gravity. It has no initial angular velocity. When it hits the ground it should have some rotation resulting from the collision.   How to calculate force that caused torque for that rotation?   Problem 2  The same disc is dropped from height. It doesn't have velocity on the side direction. It already spinning fast. When it hits the ground the spinning should cause some translation.   How to calculate force that caused this linear acceleration? Some rotation must be lost in the collision, how to calculate that?   To simplify assume static $friction = 1$ and $g = -10$. Phantom device showing on Google Play Run a command without making me wait I'm working on this problem from Elementary Analysis by Ross which is intuitive when sketched but keeps stymieing me when I try to write it out.  Let $f$ be a continuous function on $[a,b] \subset \mathbb{R}$. Define $f^\star (x)$ as:  $$ f^\star(x) = \sup \{f(y)\mid a \leq y \leq x \} $$ Prove that $f^\star$ is a continuous increasing function on $[a,b]$.  Things I've figured out: (these are mostly trivial)   $f$ is uniformly continuous on $[a,b]$. Since $[a,b]$ is closed and bounded there exists some $c \in [a,b]$ such that $f(c) \geq f(x)\ \forall x \in [a,b]$. (In words: the supremum is actually attained.) If $c \in [a,b]$ is as above, then $f^\star$ is constant (and hence continuous) on $[c,b]$ (which is possibly a singleton).   This seems completely obvious when you actually draw a continuous function but translating that to a formal proof eludes me...