Why I Miss Command-Line Programming
July 12th, 2009
Here is the HTML I’m rendering:
<?xml version=”1.0″ encoding=”utf-8″?><!DOCTYPE html PUBLIC ‘-//W3C//DTD XHTML 1.0 Strict//EN’ ‘http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd’><html xmlns=”http://www.w3.org/1999/xhtml”>
<head>
<title>Software Carpentry: Computational Complexity</title>
<meta name=”author” content=”Greg Wilson” />
<meta name=”company” content=”Third Bit” />
<meta name=”date” content=”Sun Jul 12 17:32:26 2009″ />
<link rel=”stylesheet” href=”format/style.css” type=”text/css” />
</head>
<body>
<ul>
<li>Well-developed mathematical notation.</li>
<li>For any functions f,g : ℕ → ℝ<sup>+</sup>, write f ∈ O(g) to represent "f grows on the order of g".</li>
<li>Mathematically: f(n) ≤ cg(n) for all n ≥ B, for constants c and B.</li>
<li>Intuition: f grows <em>no faster</em> than g, to within a constant factor and ignoring any finite number of exceptions.</li>
<li>For example, 2n+7 ∈ O(n) because 2n+7 ≤ 2n+7n = 9n for all n ≥ 1
<ul>
<li>But also 2n+7 ∈ O(n<sup>2</sup>) and 2n+7 ∈ O(2<sup>n</sup>), <em>etc</em>.</li>
<li>However, 2n+2 ∉ O(1).</li>
</ul>
</li>
</ul>
</body>
</html>
Here is the appearance with Firefox 3 on Windows XP:
And here is the appearance with IE7 on the same platform:
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