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197 lines
7.8 KiB
HTML
197 lines
7.8 KiB
HTML
<!DOCTYPE html>
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<html lang="en"><!-- #BeginTemplate "/Templates/Main.dwt" --><!-- DW6 -->
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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>The Language of Mathematics</title>
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<script language="JavaScript" type="text/javascript">reSpell=[["math","maths"]];</script>
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<meta name="keywords" content="math, maths, mathematics, school, homework, education">
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<div id="stt"></div>
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<div id="hdr"></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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<div id="content" role="main"><!-- #BeginEditable "Body" -->
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<h1 align="center">The Language of Mathematics</h1>
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<h2>The Language of Mathematics</h2>
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<p>The Language of Mathematics was designed so we can write about:</p>
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<div class="dotpoint">
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<p><b>Things</b> like Numbers, Sets, Functions, etc</p>
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</div>
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<div class="dotpoint">
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<p> What we <b>Do</b> with those things (add, subtract, multiply, divide, join together, etc)<br>
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</p>
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</div>
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<h2>Symbols</h2>
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<p style="float:right; margin: 10px;"><img src="images/speak-pi.jpg" alt="speak pi" height="96" width="150"></p>
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<p>Mathematics uses symbols instead of words:</p>
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<ul>
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<li>There are the 10 digits: <span class="larger">0, 1, 2, ... 9</span></li>
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<li>There are symbols for operations: <span class="larger">+, −, ×, /, ...</span></li>
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<li>And symbols that "stand in" for values: <span class="larger">x, y, ...</span></li>
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<li>And many special symbols: <span class="times">π</span><span class="larger">, =, <, ≤, ...</span></li>
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</ul>
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<h2>Letter Conventions </h2>
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<p>Letters often have special uses: </p>
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<div class="simple">
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<table align="center" border="0">
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<tbody>
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<tr>
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<th> </th>
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<th>Examples</th>
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<th>What they usually mean</th>
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</tr>
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<tr>
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<td>Start of the alphabet:</td>
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<td><b>a, b, c, ...</b></td>
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<td>constants (fixed values)</td>
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</tr>
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<tr>
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<td>From i to n:</td>
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<td><b>i, j, k, l, m, n</b></td>
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<td>positive <a href="whole-numbers.html">integers</a> (for counting)</td>
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</tr>
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<tr>
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<td>End of the alphabet:</td>
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<td align="right"><b>... x, y, z</b></td>
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<td>variables (unknowns)</td>
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</tr>
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</tbody></table>
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<p>Those are <b>not rules</b>, but they are often used that way.</p>
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</div>
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<div class="example">
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<h3>Example: <br>
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<div align="center">y = ax + b</div></h3>
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<p>People will <b>assume</b> that <span class="large">a</span> and <span class="large">b</span> are fixed values, </p>
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<p>And that <span class="large">x</span> is the one that changes, which in turn makes <span class="large">y</span> change.</p>
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</div>
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<h2>UPPERCASE vs lowercase</h2>
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<p>It is also common to use</p>
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<ul>
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<li> lowercase for variables (like x or y) or counting values (like m or n) and</li>
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<li> UPPERCASE for <a href="sets/sets-introduction.html">sets</a> (like X or Y) and special constants</li></ul>
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<div class="example">
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<h3>Example: <br>
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<div align="center">A = {1, 2, 3}</div></h3>
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<p>Using an uppercase "A" makes it easy to tell it is a set.</p></div>
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<p>It makes things clearer to read.</p>
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<h2>Nouns, Verbs, Sentences</h2>
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<p>We don't use the words "noun", "verb", or "pronoun" in Mathematics, but we can imagine these <b>similarities to English</b>:</p>
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<div class="dotpoint"> <b>Nouns</b> could be fixed things, such as numbers, or expressions with numbers:
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<div class="beach">
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<table align="center" border="0">
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<tbody>
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<tr align="center">
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<td width="80">15</td>
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<td width="80">2(3-1/2)</td>
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<td width="80">4<sup>2</sup></td>
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</tr>
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</tbody></table>
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</div>
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</div>
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<div class="dotpoint"> The <b>Verb</b> could be the equals sign "=", or an <a href="algebra/inequality.html">inequality</a> like < or > </div>
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<div class="dotpoint"> <b>Pronouns</b> (things like <i>it</i>, <i>he</i>, <i>you</i>, etc) could be variables like <b>x</b> or <b>y</b>:
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<div class="beach">
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<table align="center" border="0">
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<tbody>
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<tr align="center">
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<td width="80">5<b>x</b>-7</td>
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<td width="80"><b>xy</b><sup>2</sup></td>
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<td width="80">-3/<b>x</b></td>
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</tr>
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</tbody></table>
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</div>
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</div>
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<div class="dotpoint"> An <b>Adjective</b> could be a subscript like the "n" in x<sub>n</sub></div>
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<div class="dotpoint"> And they could be put together into a <b>Sentence</b> like this:
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<p class="large" align="center">3x + 7 = 22</p>
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<p align="center">(And we actually do use the word <a href="algebra/open-sentences.html">sentence</a> in mathematics!)</p>
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</div>
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<p> </p>
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<div class="related">
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<a href="mathematics.html">Welcome to Mathematics</a> <a href="mathematics-learning.html">Learning Mathematics</a> <a href="mathematics-help-me.html">Help! I Can't Do Mathematics!</a>
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<a href="numbers/evolution-of-numbers.html">Evolution of Numbers</a>
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<a href="math-maths-english.html">Math vs Maths</a>
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</div>
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Copyright © 2018 MathsIsFun.com
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