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more work on numbers section
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Mark Pilgrim
+63
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@@ -88,7 +88,7 @@ body{counter-reset:h1 2}
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<samp class="prompt">>>> </samp><kbd>size < 0</kbd>
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<samp>True</samp></pre>
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<h2 id="numbers">Numbers</h2>
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<p>Numbers are awesome. There are so many to choose from. Python supports both integers and floating point numbers.
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<p>Numbers are awesome. There are so many to choose from. Python supports both integers and floating point numbers. There's no type declaration to distinguish them; Python tells them apart by the presence or absence of a decimal point.
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<pre class="screen">
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<a><samp class="prompt">>>> </samp><kbd>type(1)</kbd> <span>①</span></a>
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<samp><class 'int'></samp>
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@@ -97,21 +97,64 @@ body{counter-reset:h1 2}
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<a><samp class="prompt">>>> </samp><kbd>1 + 1.0</kbd> <span>③</span></a>
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<samp>2.0</samp>
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<samp class="prompt">>>> </samp><kbd>type(2.0)</kbd>
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<samp><class 'float'></samp>
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<a><samp class="prompt">>>> </samp><kbd>1.12345678901234567890</kbd> <span>④</span></a>
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<samp><class 'float'></samp></pre>
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<ol>
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<li>You can use the <code>type()</code> function to check the type of any value or variable. As you might expect, <code>1</code> is an <code>int</code>.
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<li>Adding an <code>int</code> to an <code>int</code> yields an <code>int</code>.
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<li>Adding an <code>int</code> to a <code>float</code> yields a <code>float</code>. Python coerces the <code>int</code> into a <code>float</code> to perform the addition, then returns a <code>float</code> as the result.
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</ol>
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<p>As you just saw, some operators (like addition) will coerce integers to floating point numbers as needed. You can also coerce them by yourself.
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<pre class="screen">
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<a><samp class="prompt">>>> </samp><kbd>float(2)</kbd> <span>①</span></a>
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<samp>2.0</samp>
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<a><samp class="prompt">>>> </samp><kbd>int(2.0)</kbd> <span>②</span></a>
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<samp>2</samp>
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<a><samp class="prompt">>>> </samp><kbd>int(2.5)</kbd> <span>③</span></a>
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<samp>2</samp>
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<a><samp class="prompt">>>> </samp><kbd>int(-2.5)</kbd> <span>④</span></a>
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<samp>-2</samp>
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<a><samp class="prompt">>>> </samp><kbd>1.12345678901234567890</kbd> <span>⑤</span></a>
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<samp>1.1234567890123457</samp>
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<a><samp class="prompt">>>> </samp><kbd>type(1000000000000000)</kbd> <span>⑤</span></a>
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<a><samp class="prompt">>>> </samp><kbd>type(1000000000000000)</kbd> <span>⑥</span></a>
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<samp><class 'int'></samp></pre>
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<ol>
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<li>
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<li>
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<li>
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<li>
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<li>You can explicitly coerce an <code>int</code> to a <code>float</code> by calling the <code>float()</code> function.
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<li>Unsurprisingly, you can also coerce a <code>float</code> to an <code>int</code> by calling <code>int()</code>.
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<li>The <code>int()</code> function will truncate, not round.
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<li>The <code>int()</code> function truncates negative numbers towards <code>0</code>. It's a true truncate function, not a a floor function.
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<li>Floating point numbers are accurate to 15 decimal places.
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<li>Integers can be arbitrarily large.
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</ol>
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<blockquote class="note compare python2">
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<p><span>☞</span>Python 2 had separate types for <code>int</code> and <code>long</code>. The <code>int</code> datatype was limited by <code>sys.maxint</code>, which varied by platform but was usually <code>2<sup>32</sup>-1</code>. Python 3 has just one integer type, which behaves mostly like the old <code>long</code> type from Python 2.
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<p><span>☞</span>Python 2 had separate types for <code>int</code> and <code>long</code>. The <code>int</code> datatype was limited by <code>sys.maxint</code>, which varied by platform but was usually <code>2<sup>32</sup>-1</code>. Python 3 has just one integer type, which behaves mostly like the old <code>long</code> type from Python 2. See <a href="http://www.python.org/dev/peps/pep-0237">PEP 237</a> for details.
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</blockquote>
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<p>You can do all kinds of things with numbers.
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<pre class="screen">
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<a><samp class="prompt">>>> </samp><kbd>11 / 2</kbd> <span>①</span></a>
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<samp>5.5</samp>
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<a><samp class="prompt">>>> </samp><kbd>11 // 2</kbd> <span>②</span></a>
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<samp>5</samp>
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<a><samp class="prompt">>>> </samp><kbd>−11 // 2</kbd> <span>④</span></a>
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<samp>−6</samp>
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<a><samp class="prompt">>>> </samp><kbd>11.0 // 2</kbd> <span>③</span></a>
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<samp>5.0</samp>
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<a><samp class="prompt">>>> </samp><kbd>11 ** 2</kbd> <span>⑤</span></a>
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<samp>121</samp>
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<a><samp class="prompt">>>> </samp><kbd>11 % 2</kbd> <span>⑥</span></a>
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<samp>1</samp>
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</pre>
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<ol>
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<li>The <code>/</code> operator performs floating point division. It returns a <code>float</code> even if both the numerator and denominator are <code>int</code>s.
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<li>The <code>//</code> operator performs a quirky kind of integer division. When the result is positive, you can think of it as truncating (not rounding) to <code>0</code> decimal places, but be careful with that.
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<li>When integer-dividing negative numbers, the <code>//</code> operator rounds “up” to the nearest integer. Mathematically speaking, it's rounding “down” since <code>−6</code> is less than <code>−5</code>, but it could trip you up if you expecting it to truncate to <code>−5</code>.
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<li>The <code>//</code> operator doesn't always return an integer. If either the numerator or denominator is a <code>float</code>, it will still round to the nearest integer, but the actual return value will be a <code>float</code>.
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<li>The <code>**</code> operator means “raised to the power of.” <code>11<sup>2</sup></code> is <code>121</code>.
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<li>The <code>%</code> operator gives the remainder after performing integer division. <code>11</code> divided by <code>2</code> is <code>5</code> with a remainder of <code>1</code>, so the result here is <code>1</code>.
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</ol>
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<blockquote class="note compare python2">
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<p><span>☞</span>In Python 2, the <code>/</code> operator usually meant integer division, but you could make it behave like floating point division by including a special directive in your code. In Python 3, the <code>/</code> operator always means floating point division. See <a href="http://www.python.org/dev/peps/pep-0238/">PEP 238</a> for details.
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</blockquote>
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<p>FIXME fractions, math module, numbers in a boolean context
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<h2 id="lists">Lists</h2>
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<p>FIXME
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<h2 id="sets">Sets</h2>
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@@ -206,6 +249,17 @@ samp class="prompt">>>> </samp><kbd>a_dict</kbd>
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<samp class="prompt">>>> </samp><kbd>x == y</kbd>
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<samp>True</samp>
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</pre>
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<div class="fr">
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<h4>Further reading (FIXME)</h4>
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<ul>
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<li>fractions
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<li>math module
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<li>PEP 237
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<li>PEP 238
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<li>links to appendix
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<li>...etc...
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</ul>
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</div>
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<p class="c">© 2001-4, 2009 <span>ℳ</span>ark Pilgrim, <a rel="license" href="http://creativecommons.org/licenses/by/3.0/">CC-BY-3.0</a>
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</body>
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</html>
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