I've already enchanted all of my gear except for the knights armor and the spoon (which I don't have yet, how do you get the spoon anyways?).  The only places I haven't really discovered yet are: right door of the desert fortress, the big empty room with a chest all the way up some plateau, the spikes room in the castle, hell and the developer. Unless theres a place somewhere hidden, I don't know where to get more chocolate bars.
I've ran out of chocolate bars and didn't realize I could enchant my giant spoon and knight's armor. Is there any way to get more reliably?
I remember my professor in college challenging me with this question, which I failed to answer satisfactorily: I know there exists a bijection between the rational numbers and the natural numbers, but can anyone produce an explicit formula for such a bijection? Is there any rule for when it is better to use genitive case or noun as adjective? I'm not sure if there is any difference in meaning in this example:     The department of accounting       The accounting department   Can I also use both forms in situations like:     The restaurants of Paris / The Paris restaurants      The room window / The window of the room How to Prevent the System.QueryException I am getting "Error System.QueryException: List has no rows for assignment to SObject".   Line 1: Account ac = [select id from Account where name='testaccount' limit 1] Line 2: if(ac != null) {           //do something         }   I got the above error in line 2 if there is no record.   Any help? I have a vector space $V$ over a field of characteristic $0$. If $M_1,\dots,M_k$ are proper subspaces of $V$, and $N$ is a subspace of $V$ such that $N\subseteq M_1\cup\cdots\cup M_k$, how can you tell $N\subseteq M_i$ for some $i$?  I was first trying to show it just in the case $N\subseteq M_1\cup M_2$, and hoping to extend it to finitely many $M_i$. If either of the $M_i$ contains the other, the claim follows, so I suppose neither $M_i$ contains the other.   In hopes of a contradiction, I suppose $N\not\subseteq M_1$ and $N\not\subseteq M_2$, Picking $x_1\in N\setminus M_1$ and $x_2\in N\setminus M_2$, I'd have $x_1+x_2\in N\subseteq M_1\cup M_2$. The only thing I could conclude was that actually $x_1,x_2\notin M_1$ and $x_1,x_2\notin M_2$, which seems like a dead end. What's the right way to do this? I want to limit some users daily computer usage on the family PC. Currently we only have one user account set up on it, but I could create new ones. So Is there a way to set daily time limits for user on a windows 7 PC? Ideally I would like to set up it up for 2 hours on weekdays and 3 hours on weekends. How to implement a follow author (or user) function? Is it possible to implement a Follow button for authors of posts in Drupal 7, so that users can:   Follow any one they wish, and Be notified about the new posts of those authors.   This sounds like 'Mashable Follow button' for authors.  Do you have any suggestions about how to implement this? Conformally Map Region between tangent circles to Disk Proper use of the IDisposable interface MacBook [Pro] - how many displays, what resolution/frequency? Prove that $p \in \mathbb{R}[x]$ can be represented as a sum of squares of polynomials from $\mathbb{R}[x]$ When I try to save a new file in TextEdit, I always get a popup saying I can't save with ".txt" at the end of the file name.  I want to save a plaintext file, but TextEdit insists on saving as .rtf instead. It also lists .doc, .odt, .html, and some others.  How can I save a TextEdit document as plain text? ISP blocking port 25 I've already done a lot of searching (in particular: ) to try to prove this statement:      $f: A \to B$ is injective if and only if it has a left inverse. [I'm going to also assume $A$ and $B$ are nonempty.]   My attempt so far:     $\Leftarrow$ Suppose $f$ has a left inverse and $f(a_1) = f(a_2)$ for    $a_1, a_2 \in A$. Then there is a function $g: B \to A$ such that   $g\left(f(a_1)\right) = a_1$ and $g\left(f(a_2)\right) = a_2$. Since   $g$ is well-defined, it follows that $g\left(f(a_1)\right) =  g\left(f(a_2)\right)$, and hence $a_1 = a_2$.         $\Rightarrow$Now   suppose $f$ is injective. Then $f(a_1) = f(a_2) \implies a_1 = a_2$.   Furthermore, since $A$ is nonempty, there is an element $x \in A$.   Define $g: B \to A$ by  \begin{equation*} g(b) = \begin{cases}  f^{-1}(b), &amp; b \in \text{Im}(f) \\ x, &amp; b \in A \setminus  \text{Im}(f)\text{.} \end{cases} \end{equation*} This mapping is   well-defined, since if $f$ is injective, $f^{-1}(b)$ is unique.   My main question: does this imply that if $f: A \to B$ is injective that any mapping $g: \text{Im}(f) \to A$ is bijective? Otherwise, I don't understand why we can even use $f^{-1}$ on an element. [Please read the link above for more details - in proof 1.] What is the integral of 0? Given two equivalent norms, convergence in one implies convergences in other. Suppose we have two equivalent norms, $\|\cdot \| \sim \left\vert\!\left\vert\!\left\vert \cdot\right\vert\!\right\vert\!\right\vert$. We assume that $x_n \rightarrow x $ in $(X,\|\cdot \|)$. Show that $x_n \rightarrow x $ in $(X,\left\vert\!\left\vert\!\left\vert \cdot\right\vert\!\right\vert\!\right\vert)$  We observe since the norms are equivalent, there exits constants $\alpha, \beta$, such that $\alpha \|\cdot \| \leq \left\vert\!\left\vert\!\left\vert \cdot\right\vert\!\right\vert\!\right\vert \leq \beta \|\cdot \|$, with $0 \lt \alpha \leq \beta$  Since, $x_n \rightarrow x$ in $(X,\|\cdot \|$) we know that for all $\epsilon&gt;0, \exists K(\epsilon)$ such that for n>$K(\epsilon),$ we have $\|x_n -x\| \leq \epsilon$  Since, we know $\beta \gt 0$ , then $ \beta \|x_n -x\| \leq \beta \epsilon$, Thus we see that $\left\vert\!\left\vert\!\left\vert x_n-x\right\vert\!\right\vert\!\right\vert\leq \beta \epsilon$.  This is how far I've gotten, our goal to is to find a a $J(\epsilon)$ such that for all $\epsilon&gt;0, \exists J(\epsilon)$ such that for n>$J(\epsilon),$ we have $\left\vert\!\left\vert\!\left\vert x_n-x \right\vert\!\right\vert\!\right\vert \leq \epsilon$  My candidate for $J(\epsilon$) is $J(\epsilon) = \frac{K(\epsilon)}{\beta}$ from my above argument, but I'm not exactly sure how to validate this. If someone could help me on the proof, it would be very appreciated. I believe I'm pretty close, just missing something small. RSA encryption with private key and decryption with a public key When using the RSA cryptosystem, does it still work if you instead encrypt with the private key and decrypt with the public key? What about in the case of using RSA for sender authentication? How can I check for an empty/undefined/null string in JavaScript? I saw , but I didn't see a JavaScript specific example. Is there a simple string.Empty available in JavaScript, or is it just a case of checking for ""? Transfer / security in Istanbul Ataturk airport after 29/06/2016 How can I configure the Ubuntu Dock to show windows only from the current workspace? Algebraic Proof that $\sum\limits_{i=0}^n \binom{n}{i}=2^n$