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making html validate

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commit 877faf2c678f49031fb318f715f12ae93bd3e0e6 1 parent 3297ace
Ben Crowell authored
Showing with 18 additions and 15 deletions.
  1. +18 −15 index.html
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33 index.html
@@ -1,5 +1,8 @@
+<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN" "http://www.w3.org/TR/html4/strict.dtd">
<html>
-<head><title>Inf -- a calculator that can handle infinite and infinitesimal numbers</title></head>
+<head><title>Inf -- a calculator that can handle infinite and infinitesimal numbers</title>
+<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
+</head>
<body onload = "set_up();">
<h1>Inf</h1>
@@ -12,14 +15,14 @@
<div id="terminal" style="width:100%; height:600px;"></div>
- <script src="Terminal.js"></script>
- <script src="Lexer.js"></script>
- <script src="Parser.js"></script>
- <script src="Num.js"></script>
- <script src="Complex.js"></script>
- <script src="Rational.js"></script>
- <script src="LeviCivita.js"></script>
- <script>
+ <script src="Terminal.js" type="text/javascript"></script>
+ <script src="Lexer.js" type="text/javascript"></script>
+ <script src="Parser.js" type="text/javascript"></script>
+ <script src="Num.js" type="text/javascript"></script>
+ <script src="Complex.js" type="text/javascript"></script>
+ <script src="Rational.js" type="text/javascript"></script>
+ <script src="LeviCivita.js" type="text/javascript"></script>
+ <script type="text/javascript">
function set_up() {
var lexer = new com.lightandmatter.Lexer({});
var parser = new com.lightandmatter.Parser({});
@@ -45,23 +48,24 @@
</p>
<p>
Predefined constants:
+</p>
<ul>
<li> i -- the square root of -1
<li> pi -- the ratio of a circle's circumference to its diameter
<li> d -- an infinitesimally small number
</ul>
-</p>
<p>
Built-in operators:
+</p>
<ul>
<li> : -- assigns the expression on the right to the variable named on the left-hand side
<li> =, <, > -- comparisons
<li> +, -, *, / -- arithmetic
<li> ^ -- exponentiation
</ul>
-</p>
<p>
Built-in functions:
+</p>
<ul>
<li> sin, cos, tan
<li> asin, acos, atan
@@ -69,7 +73,6 @@
<li> exp, ln
<li> floor, ceil
</ul>
-</p>
<p>
Inf represents infinite and infinitesimal quantities as <a href="http://en.wikipedia.org/wiki/Levi-Civita_field">Levi-Civita numbers</a>.
The Levi-Civita numbers obey all the same <a href="http://en.wikipedia.org/wiki/First-order_logic">elementary</a> axioms of arithmetic as the real numbers.
@@ -82,6 +85,7 @@
</p>
<p>
Here are some examples you can try in the calculator to get a feeling for how all this works:
+</p>
<ul>
<li> 1/0 ... undefined
<li> 1/d ... gives an infinite result
@@ -89,15 +93,14 @@
<li> 2/d+1 ... and an even bigger infinity
<li> d>0 ... true
<li> d<10^-10 ... true
-<li> d^2<d ... true, showing that we have different sizes of infinity
-<li> d^2>0 ... true, because even though d^2 is infinitesimally small compared to d, it's still no zero
+<li> d^2&lt;d ... true, showing that we have different sizes of infinity
+<li> d^2&gt;0 ... true, because even though d^2 is infinitesimally small compared to d, it's still no zero
<li> sqrt(d)
<li> sqrt(d)>d ... true
<li> 1/(1-d) ... is calculated using the <a href="http://en.wikipedia.org/wiki/Geometric_series">geometric series</a>, up to a certain level of precision
<li> exp(d) ... is calculated using a <a href="http://en.wikipedia.org/wiki/Taylor_series">Taylor series</a>
<li> exp(1/d) ... is undefined in the Levi-Civita system
</ul>
-</p>
<p>
Calculus students often get the impression that the notion of an infinite or infinitesimal number can never be defined in any rigorous or
self-consistent way. That's not true. Tullio Levi-Civita defined the Levi-Civita numbers around 1900, so it's been known for over a
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