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189 lines
7.2 KiB
HTML
189 lines
7.2 KiB
HTML
<!DOCTYPE html>
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<html lang="en"><!-- #BeginTemplate "/Templates/Main.dwt" --><!-- DW6 -->
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<!-- Mirrored from www.mathsisfun.com/whole-numbers.html by HTTrack Website Copier/3.x [XR&CO'2014], Sat, 29 Oct 2022 00:35:38 GMT -->
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<meta http-equiv="content-type" content="text/html; charset=UTF-8">
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<!-- #BeginEditable "doctitle" -->
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<title>Whole Numbers and Integers</title>
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<meta name="keywords" content="math, maths, mathematics, school, homework, education">
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<div id="hdr"></div>
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<div class="mid">
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<div id="menuWide" class="menu"></div>
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<div id="logo"><a href="index.html"><img src="images/style/logo.svg" alt="Math is Fun"></a></div>
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<article id="content" role="main">
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<!-- #BeginEditable "Body" -->
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<h1 class="center">Whole Numbers and Integers</h1>
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<h2>Whole Numbers</h2>
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<p>Whole Numbers are simply the numbers <b>0, 1, 2, 3, 4, 5, ...</b> (and so on)</p>
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<p class="center"><img src="numbers/images/number-line-whole.svg" alt="number line whole" height="69" width="443"><br>
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No Fractions!</p>
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<div class="example">
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<h3>Examples: 0, 7, 212 and 1023 are all whole numbers</h3>
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<p>(But numbers like ½, 1.1 and −5 are <b>not</b> whole numbers.)</p>
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</div>
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<h2>Counting Numbers</h2>
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<p>Counting Numbers are Whole Numbers, but <b>without the zero</b>. Because you can't "count" <a href="numbers/zero.html">zero</a>.</p>
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<p class="center"><img src="numbers/images/number-line-counting.svg" alt="number line whole" height="69" width="443"></p>
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<p>So they are <b>1, 2, 3, 4, 5, ...</b> (and so on).</p>
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<h2>Natural Numbers</h2>
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<p>"Natural Numbers" can mean either "Counting Numbers" {1, 2, 3, ...}, or "Whole Numbers" {<b>0</b>, 1, 2, 3, ...}, depending on the subject.</p>
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<h2>Integers</h2>
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<p>Integers are like whole numbers, but they <b>also include negative numbers</b> ... but still no fractions allowed!</p>
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<p class="center"><img src="numbers/images/number-line.svg" alt="number line -10 to 10" height="47" width="595"></p>
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<p>So, integers can be negative {−1, −2,−3, −4, ... }, positive {1, 2, 3, 4, ... }, or zero {0}</p>
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<p>We can put that all together like this:</p>
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<p class="center"><span class="larger">Integers = { ..., −4, −3, −2, −1, 0, 1, 2, 3, 4, ... }</span></p>
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<div class="example">
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<h3>Examples: <span class="larger">−16, −3, 0, 1 and 198 </span> are all integers.</h3>
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<p>(But numbers like ½, 1.1 and 3.5 are <b>not</b> integers)</p>
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</div>
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<p class="larger">These are all integers (click to mark), and they continue left and right infinitely:</p>
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<div class="script" style="height: 150px;">
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numbers/images/number-line.js?mode=int
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</div>
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<h2>Some People Have Different Definitions!</h2>
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<p><i><b>Some</b></i> people (not me) say that whole numbers can also be negative, which makes them
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exactly the same as integers.</p>
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<p><i><b>And</b></i> some people say that zero is NOT a whole number. So there you
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go, <i>not everyone agrees on a simple thing!</i></p>
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<h2>My Standard</h2>
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<p>I usually stick to this:</p>
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<div class="simple">
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<table>
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<tbody>
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<tr>
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<td>
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<div class="center"><b>Name</b></div></td>
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<td>
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<div class="center"><b>Numbers</b></div> </td>
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<td>
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<div class="center"><b>Examples</b></div> </td>
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</tr>
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<tr>
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<td>
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<div class="center large">Whole Numbers</div></td>
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<td>
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<div class="center large">{ 0, 1, 2, 3, 4, ... }</div> </td>
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<td style="text-align:center;">0, 27,398, 2345 </td>
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</tr>
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<tr>
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<td>
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<div class="center large">Counting Numbers</div></td>
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<td>
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<div class="center large">{ 1, 2, 3, 4, ... }</div> </td>
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<td style="text-align:center;">1, 18, 27, 2061 </td>
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</tr>
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<tr>
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<td>
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<div class="center large">Integers</div></td>
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<td>
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<div class="center large">{ ... −4, −3, −2, −1, 0, 1, 2, 3, 4, ... }</div> </td>
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<td style="text-align:center;">−15, 0, 27, 1102 </td>
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</tr>
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</tbody></table>
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</div>
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<p>And everyone agrees on the definition of an <b>integer</b>, so when in doubt say "integer".</p>
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<p>And
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when you only want positive integers, say "positive integers". It is not only accurate, it makes you
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sound intelligent. Like this (note: zero isn't positive or negative):</p>
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<ul>
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<li>Integers = { ..., −4, −3, −2, −1, 0, 1, 2, 3, 4, ... }</li>
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<li>Negative Integers = { ..., −4, −3, −2, −1 }</li>
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<li>Positive Integers = { 1, 2, 3, 4, ... }</li>
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<li>Non-Negative Integers = { 0, 1, 2, 3, 4, ... } <i>(includes zero, see?)</i></li>
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</ul>
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<h2>Other Numbers</h2>
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<p>For an interesting look at other types of numbers read <a href="numbers/evolution-of-numbers.html">The Evolution of Numbers</a></p>
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<div class="questions">422,423, 1058, 1059, 2988, 2989, 3980, 3981, 3982, 5346</div>
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<div class="related">
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<a href="number-line.html">Number Line</a>
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<a href="positive-negative-integers.html">Adding and Subtracting Positive and Negative Numbers</a>
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<a href="numbers/index.html">Number Index</a>
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<a href="algebra/index.html">Algebra Index</a>
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</div>
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</article>
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