Finding the sum of the elements of an array, Java
Is floating point math broken?
Please rate and comment. I want to improve; constructive criticism is highly appreciated. Please take style into account as well.  The following proof is solely based on vector space related axioms. Axiom names are italicised. They are defined in Wikipedia (see vector space article).  Vector spaces - Multiplying by zero scalar yields zero vector  \begin{array}{lrll} \text{Let} &amp; \dots &amp; \text{be} &amp; \dots \\ \hline &amp; F &amp;&amp; \text{a field.} \\ &amp; V &amp;&amp; \text{a vector space over $F$.} \\ &amp; 0 &amp;&amp; \text{an identity element of addition of $F$.} \\ &amp; \mathbf{0} &amp;&amp; \text{an identity element of addition of $V$.} \\ &amp; \mathbf{v} &amp;&amp; \text{an arbitrary vector in $V$.} \\ \end{array}  $$\text{Then, }0\mathbf{v} = \mathbf{0}.$$  Proof. We will denote by $1$ an identity element of scalar multiplication; we will denote by $(-\mathbf{v})$ an additive inverse of $\mathbf{v}$. \begin{align*} 0\mathbf{v} &amp;= 0\mathbf{v} + \mathbf{0}                     &amp;&amp; \text{by }\textit{Identity element of vector addition} \\ &amp;= 0\mathbf{v} + (\mathbf{v} + (-\mathbf{v}))   &amp;&amp; \text{by }\textit{Inverse elements of vector addition} \\ &amp;= (0\mathbf{v} + \mathbf{v}) + (-\mathbf{v})   &amp;&amp; \text{by }\textit{Associativity of vector addition} \\ &amp;= (0\mathbf{v} + 1\mathbf{v}) + (-\mathbf{v})  &amp;&amp; \text{by }\textit{Identity element of scalar multiplication} \\ &amp;= ((0 + 1)\mathbf{v}) + (-\mathbf{v})          &amp;&amp; \text{by }\textit{Distributivity of scalar multiplication (field addition)} \\ &amp;= ((1 + 0)\mathbf{v}) + (-\mathbf{v})          &amp;&amp; \text{by }\textit{Commutativity of field addition} \\ &amp;= (1\mathbf{v}) + (-\mathbf{v})                &amp;&amp; \text{by }\textit{Identity element of field addition} \\ &amp;= \mathbf{v} + (-\mathbf{v})                   &amp;&amp; \text{by }\textit{Identity element of scalar multiplication} \\ &amp;= \mathbf{0}                                   &amp;&amp; \text{by }\textit{Inverse elements of vector addition} \\ \end{align*} QED I've downloaded the new iOS 8 update on my iPhone 5 but am getting second thoughts about actually installing it.  Is there a way for me to delete that download or am I at the point of no return? How can I automatically save screen shots by the press on the Prt Scr button? I want a screen shot to be saved automatically to a location I specify, as soon as I press the Prt Scr button on my keyboard, or the Alt+Prt Scr combo. I also want the date and time to be used as file name for each new screen shot. And I want the files to be saved as PNG images.  Is there a Windows program that would allow me to do just this? I don't want any other fancy features like editing and making notes, etc. just a plain simple program that will either automatically save the screen shots to a pre-set location or prompt me where I want to save it. I don't want to go through MS Paint to save the shots.  I guess what I'm after is a little bit of Linux behavior of Print Screen, but only for Windows. And I additionally want the files to be named by the date and time they were taken.  Update:  Meanwhile, I have found one called Greenshot. But I don't know how to get the file name pattern right.  This is the default pattern.  ${capturetime:d"yyyy-MM-dd HH_mm_ss"}-${title}   Can someone explain this? Why do they have the title capturetime and the quotation marks? It produces file names like this.  2013-01-26 15_24_28-Greenshot.png   And this is what it says about the file patterns in the program description.  ${YYYY} year, 4 digits ${MM} month, 2 digits ${DD} day, 2 digits ${hh} hour, 2 digits ${mm} minute, 2 digits ${ss} second, 2 digits ${NUM} incremental number, 6 digits ${title} Window title ${user} Windows user ${domain} Windows domain ${hostname} PC name   How do I get files that include year, month and day, separated by a dash, followed by hour, minute and second? I want to include a time for uniqueness of the file name. This is a minor frustration, but I have a  that I put italics and bold into (using asterisks.)  Now I know I just just be happy that I could do it at all, but it seems to me that those should not count toward my comment char limit. There are numerous (, , ) questions concerning this problem. I realize this is a borderline duplicate, but I'll re-iterate the futility of this particular filter and why it should be outright removed from Stack Overflow.  Do you know how effective this is in preventing users who just don't care from posting questions with bad titles? 100% ineffective. What do these users do?   Replace it with a synonym: "issue," "trouble," "predicament," "botheration" or what have you. Or worse, they simply work around the filter by deliberately misspelling the word or inserting space or punctuation:    () ?    and the coup de grâce:      I mean, even Jeff . This adds zero value to the title. In fact, it looks worse. Why, oh why are people  to scrap a bad feature? All this does is:   Prevent people who have a  to use the word "problem" in the title from posting questions with an appropriate title. Break the search feature because of workarounds or the need to use less descriptive titles than the error itself   This is an extraordinarily useless (and harmful) feature. Please, for the love of Cthulhu,  remove, eliminate, abolish, eradicate, extirpate this "feature" from Stack Overflow.    Bonus:     So I can't mention the Halting Problem in the title? – Keith Thompson Nov 1 at 19:05      @KeithThompson Maybe it's a "Halting Issue". Or "Need help with Halting". Or the "Halting thing in Computability Theory". – slhck Nov 1 at 19:14 Address is invalid on local machine [on windows 8 only] When is "self" required? I have been using classes for only a short while and when I write a method, I make all variables reference self, e.g. self.foo.  However, I'm looking through the wxPython in Action book and notice that "self" isn't used all the time. For example:   import wx  class TextFrame(wx.Frame):     def __init__(self):         wx.Frame.__init__(self, None, -1, 'Text Entry Example',             size=(300, 100))         panel = wx.Panel(self, -1)         basicLabel = wx.StaticText(panel, -1, "Basic Control:")         basicText = wx.TextCtrl(panel, -1, "I've entered some text!",             size=(175, -1))         basicText.SetInsertionPoint(0)         pwdLabel = wx.StaticText(panel, -1, "Password:")         pwdText = wx.TextCtrl(panel, -1, "password", size=(175, -1),             style=wx.TE_PASSWORD)         sizer = wx.FlexGridSizer(cols=2, hgap=6, vgap=6)         sizer.AddMany([basicLabel, basicText, pwdLabel, pwdText])         panel.SetSizer(sizer)   The one below does use "self".  import wx class ButtonFrame(wx.Frame):     def __init__(self):         wx.Frame.__init__(self, None, -1, 'Button Example',             size=(300, 100))         panel = wx.Panel(self, -1)         self.button = wx.Button(panel, -1, "Hello", pos=(50, 20))         self.Bind(wx.EVT_BUTTON, self.OnClick, self.button)         self.button.SetDefault()     def OnClick(self, event):         self.button.SetLabel("Clicked")   If I remember correctly, "self" is reference to a particular instance of the class, so when is it not necessary? Is there a general rule of thumb? Windows 10 doesn't shut down properly How to pass the password to su/sudo/ssh without overriding the TTY? Where are packages stored installed with APT in Ubuntu 16.04? My international conference in Europe this May has been canceled due to the COVID-19. I have a ticket, purchased from TAP air Portugal, from Toronto, Canada to Lisbon. Because it is a non-refundable fare, they don't want to give a refund.  They won't allow me to reschedule later than May 31 of this year. This won't be useful for me.  What options do I have? I'd prefer to get a full refund.  (I am a US citizen if it matters)  Note: They offered to refund just the taxes, which is about 10% of the value. That's not horrible, but I'd rather have the whole thing returned. Asymptotic expansion for Fresnel Integrals If you take the fresnel integrals to be $$S(x) = \int_{0}^{x}\sin \left(\frac { \pi \cdot  t^2}{2} \right) dt$$ How do you find the asymptotic expansion? I know it begins with a $1/2$ but how? When should you use generator expressions and when should you use list comprehensions in Python?  # Generator expression (x*2 for x in range(256))  # List comprehension [x*2 for x in range(256)] Is there a way to turn option strict off for just a single line of code?    I'm doing some maintenance work and I need to "cheat" in just one place and I don't want to lower the standard for the entire file. What is the difference between linear equation and linear regression? I am using linear equation to find the correlation of values of x, y and z  3x + 4y + 2z = 6 4x + 1y + 4z = 17 8x + 2y + 5z = 9   I would like to know the difference between linear equation and linear regression. Is it the same in approach? Please add a system to allow file uploads attached to questions and answers I posted a question and a couple of respondents asked for the source code. I could only post portions of the code.  If attachments were allowed I could have uploaded a .zip file with the whole application.  Will this be a feature in SO? windows bat file error Q&A blank in Stack Exchange Android app v1.0.95 - S10e/Android 10 Recently upgraded to a Samsung S10e and Android 10, but all Q&amp;A in the Stack Exchange app v1.0.95 are blank.  The title and comments are visible, but question/answer posts are just white space. Accessing the About page in the app is also blank.  I tried clearing data, cache and re-installing the app, but I still get the same behaviour. Check existence of input argument in a Bash shell script Given a set $\{1,2,3,4\}$, how is the following relation $R$ antisymmetric?  $$R = \{(1, 2), (2, 3), (3, 4)\}$$  Note: Antisymmetric is the idea that if $(a,b)$ is in $R$ and $(b,a)$ is in $R$, then $a = b$. In my textbook  it says the above is antisymmetric which isn't the case as whenever $(a,b)$ is in $R$, $(b,a)$ is not.