VB.NET control with the same event handlers
How can I make a single event handler handle ALL Button.Click events?
This is an exercise from Chapter 3 of Golan's linear algebra book.  Problem: Show $\mathbb{Z}$ is not a vector space over a field.  Solution attempt:  Suppose there is a such a field and proceed by contradiction. I will write multiplication $FV$, where $F$ is in the field and $V$ is an element of $\mathbb{Z}$.   First we rule out the case where the field has characteristic 2. We would have   $$0=(1_F+1_F)1=1_F1+1_F1=2$$  a contradiction.  Now, consider the case where the field does not have characteristic 2. Then there is an element $2^{-1}_F$ in the field, and   $1=2_F(2^{-1}_F1)=2^{-1}_F1+2^{-1}_F1$  Now $2^{-1}_F1\in\mathbb{Z}$ as it is an element of the vector space, but there is no element $a\in\mathbb{Z}$ with $2a=1$, so we have a contradiction.  Is this correct? Is it a wise-decision to buy full-frame lenses for use on an APS-C body? I have a Canon 550D which I've been using for around a year now. I really love it and have learned a great deal with this and the 18 - 135mm kit lens. But now with experience I feel the need to get some better glass. I won't be buying a new body any time soon because I figure investing in some good glass is more important.   As I have looked around, I see quite a few good used L lenses I can get in ebay for good bargain prices. But I know that the EF lenses don't have the same focal length in the cropped sensors. Is it a wise decision to buy these EF lenses or buy the cropped sensor alternatives?  I have the following lenses in mind that I am looking to buy down the line from the canon range over the next several months.  16-35mm f/2.8L, 24-70mm f/2.8L, 70-200 f/4L.  Are these apt choices for cropped sensors? I know most pros with FFs use these but I am a bit skeptic that they will serve the same purpose for me. If so what are the alternatives for this that have almost as good image quality? What limits a motherboard from supporting more memory? My specific question is with the ASUS M3N78-VM motherboard that my home server uses. I currently have 4x2GB installed for a total of 8GB but I was hoping to upgrade to say 16GB (4x4GB). The official specifications of that motherboard says it only supports up to 8GB but it was released back when only 2GB sticks were available. What, if any, would prevent it from working with 4GB sticks now that 4GB sticks are available?  My general question is with motherboards in general... what would prevent a motherboard from working with bigger sticks if its all just the same type (DDR2 for example and same speeds) of memory? How to verify $H\otimes K \cong \bigoplus\limits_{i\in I}H$ Let $H,~K$ be the Hilbert space. if $\{v_{j}\}_{j\in J}\subset H$ and $\{w_{i}\}_{i\in I}\subset K$ are the orthonormal bases, then how to construct the isomorphic mapping: $H\otimes K \rightarrow \bigoplus\limits_{i\in I}H$. Here, the $H \otimes K$ is the tensor product of two Hilbert space. Why use a certain measure of forecast error (e.g. MAD) as opposed to another (e.g. MSE)? MAD = Mean Absolute Deviation MSE = Mean Squared Error  I've seen suggestions from various places that MSE is used despite some undesirable qualities (e.g. , which states on p8 "It is commonly believed that MAD is a better criterion than MSE. However, mathematically MSE is more convenient than MAD.")  Is there more to it than that? Is there a paper that thoroughly analyzes the situations in which various methods of measuring forecast error are more/less appropriate? My google searches haven't revealed anything.   A similar question to this was asked at , and the user was asked to post on stats.stackexchange.com, but I don't think they ever did. MS SQL Server: Do multiple queries in a batch ever execute in parallel and if so what happens when the second query is dependent on the first? How to add Android Studio to the launcher? $\prod_{k=0}^{\infty} \cos(x \cdot 2^{-k}).$ Task is to find $$\prod_{k=0}^{\infty} \cos(x \cdot 2^{-k}).$$  I tried to make it with double-angle formula: $\prod_{k=0}^{\infty} \cos(x \cdot 2^{-k}) = \frac{\prod_{k=0}^\infty \sin(x2^{1-k})}{2^\infty \cdot \prod_{k=0}^\infty \sin(x \cdot 2^{-k})} $ I'm sad to admit, that I'm stuck with that one. So I would appreciate any help, such as pointing the right direction. Is there a difference between “?!” and “!?”? What are these  error below ?  Package natbib Warning: Citation `Krishna2014' on page 16 undefined on input li ne 502.  [16 &lt;./figure/aks smr.png&gt;] [17] [18] ! Undefined control sequence. l.560 \Bibliography                    {figure/bib} Ubuntu n00b here.  I have created several disasters of the first order already.  I am getting ready to try to install opera - it is a very long and arduous process.  I am afraid - no - I am absolutely certain that I will damage something important.  How do I create a system restore point?  Does such a thing exist? Unintentional Lies and Misinformation I am trying to prove:     $a\mid b \land b\mid c \Rightarrow a\mid c $   $a\mid b$ means that a divides b if there is an integer k, that $b=k\cdot a$  Please give me a hint on how to start, because I have no idea. Objects not rotating with each other (Rubik's cube) Unexpected gaps in IDENTITY column Could someone provide me with a good explanation of why $0^0=1$?  My train of thought:  $x&gt;0$  $0^x=0^{x-0}=0^x/0^0$, so  $0^0=0^x/0^x=\,?$  Possible answers:   $0^0\cdot0^x=1\cdot0^0$, so $0^0=1$ $0^0=0^x/0^x=0/0$, which is undefined   PS. I've read the  on mathforum.org, but it isn't clear to me. Should +1 and thanks comments be a declined flag? As a moderator for GD.SE I was always led to believe our role is to clean old comments as they are intended to be a temporary item depending on the level of context and if they add any benefit to an answer.  On SO I haven't had any issues or declines when I read old Q&amp;As and see +1 and thanks and flag.    However, on other sites when I read an old Q&amp;A and I see thanks or +1 I try to be courteous and flag them as I am aware moderators do get measured by their cleanup and I'm accustomed in doing so on SO but these flags are declined.    So this leads me to ask:   Should +1 and thanks comments be flagged and is the intended role of a comment still to be considered as temporary? What is the proper classification for a thanks or +1 comment if it should be flagged?   I didn't see any Q&amp;As on this topic after browsing the tags:   and searching led me to:  but that was several years old. I'm looking to create a simple short-lived reservation system, and I'd like to generate confirmation numbers that are   unique random-looking alphanumeric short-ish, at least much shorter than 32 character-long strings returned by sha1   I'm only looking to have ~500 reservations, so I don't imagine high likelyhood of collissions.  One idea I had is generate an sha1 hash based on a date-time stamp and username, then truncating it to its first 10 characters.  Would something like that be reliably unique enough for the purposes of processing ~500 reservations? Let $a\ge 2$ be an integer. Show that for positive integers $m,n$, we have $a^n - 1$ divides $a^m - 1$ if and only if $n$ divides $m$.   I am having trouble showing this. I've seen a similar problem on here but it only shows one direction for the proof. I would like to see both directions.  This is what I have so far: Let $m = nq + r$, then $a^m - 1 = a^{nq + r}- 1 = a^{nq}a^r - 1 = a^{nq}a^r - a^r + a^r - 1 = a^r(a^{nq} - 1) + a^r - 1$. Since $0\le r\lt n$, $r = 0$ then $a^m - 1$ = $a^{nq} - 1$ so $a^m$ = $a^{nq}$ . Thus $m = nq$ hence $n\mid m$. Concatenating numbers and adding in leading zeros? I have three text fields populated as follows: 1, 9, 1 that I need to concatenate into a field that looks like 01.09.01.  Getting to 1.9.1 is easy but can anyone help out with how to formulate it so that each value has two places (i.e. add in those zeroes).  I used to do this in Excel but can't figure out how to work in ArcMap 10.