Computer Science, Finance, Mathematics

It would be nice if errors in a program are shown at once.  Unfortunately, (I think) Python's error outputs are structured so that a line by line error messages are shown.    I think the "one-by-one" error message is shown because we are using Python as the programing language. Because 1) Python is an 'interpreter' language, 2) an interpreter language translates a code line by line into a machine language, 3) a machine executes a line by line, 4) when a line contains an error, then the machine stops executing and presents an error message.    I also think the youtube video below helps how an interpreter language (like Python) presents an error message ( https://www.youtube.com/watch?v=3iLUls6Z_tw - title: compiler vs interpreter)   

If anyone attempts to install Sublime Text, faces an error message [WinError 2], and notices your Python code does not work (like I did), I suggest you to do the following: (note: I am working this on Windows 10)  Situation: error message on my computer when I run "Build" by pressing ctrl+B  1. Make sure your Python code is saved (e.g. I saved my HelloWorld.py file on my C:\Brian\PythonLab)  2. Go to Tools > Build System > New Build System 3. on the untitled.sublime-build, type the following {     "cmd": ["( your directory for Python goes here )", "-u", "$file"],     "file_regex": "^[ ]*File \"(...*?)\", line ([0-9]*)",     "selector": "source.python" } In my case, I installed Python 2.7 on the directory C:\python27 Note that the directory should be represented using double \ (\\).  That is, C:\\Python27\\python.exe  So in my case: { "cmd": ["C:\\Python27\\python.exe...

Prove: $|x+y| \leq|x|+|y|$ (triangle inequality)  $x y \leq|x y|$  $\Leftrightarrow  x y \leq|x||y|$  $\Leftrightarrow  2 x y \leq 2|x||y|$ $\Leftrightarrow  x^2+y^2+2 x y \leq x^2+y^2+2|x||y|$  $\Leftrightarrow x^2+y^2+2 x y \leq\left.| x\right|^2+|y|^2+2|x||y|$  $\Leftrightarrow  (x+y)^2 \leq(|x|+|y|)^2$ [equation 1] case 1) if $x+y>0$ then $|x+y| = x+y$  [equation1] $\Rightarrow (|x+y|)^2 \leq(|x|+|y|)^2$ [equation 2] $\Leftrightarrow |x+y| \leq|x|+|y|$  case 2) if $x+y<0$ then $|x+y| = -(x+y)$  note that $(-(x+y))^2 = (x+y)^2 = |x+y|^2$ $\Rightarrow$ [equation 2] $\Rightarrow$ $|x+y| \leq|x|+|y|$ $\blacksquare$ Published on: January 10, 2023  By: ComputeFinance