Classification of numbers by apteacher

mathematics · @apteacher · Apr 12 '18

$9.52

Classification of numbers

<html>
<h1><img src="https://imgoat.com/uploads/5b9eea6e1c/104035.png" width="495" height="267"/></h1>
<p><a href="https://i.pinimg.com/originals/a9/83/a7/a983a7b0b53f0771207fa566159fe26e.jpg">Source</a></p>
<h1>We can classify numbers as follow:</h1>
<h2>Natural numbers:</h2>
<ul>
  <li>Numbers from 1 until infinity</li>
  <li>Natural numbers are all positive numbers</li>
</ul>
<p>The set of natural numbers:</p>
<p><img src="https://imgoat.com/uploads/9e1074f5b3/103989.png" width="210" height="31"/></p>
<p><br></p>
<h2>Whole numbers:</h2>
<ul>
  <li>Numbers from 0 until infinity</li>
  <li>Whole numbers are all positive</li>
</ul>
<p>The set of whole numbers:</p>
<p><img src="https://imgoat.com/uploads/9e1074f5b3/103992.png" width="160" height="30"/></p>
<h2>Integers:</h2>
<ul>
  <li>Integers are numbers that include all the positive and the negative whole numbers plus 0 (zero)</li>
</ul>
<p>The set of integers:</p>
<p><img src="https://imgoat.com/uploads/5b9eea6e1c/104010.png" width="229" height="35"/></p>
<h2>Not all numbers can be written as natural, whole numbers or integers. &nbsp;Therefore the need for:</h2>
<p><br></p>
<h3>Rational numbers:</h3>
<ul>
  <li>Rational numbers are numbers that can be written in the form: <img src="https://imgoat.com/uploads/5b9eea6e1c/104013.png" width="30" height="44"/>&nbsp;where b ≠ 0.</li>
  <li>These numbers include all the integers, common fractions, improper fractions, mixed numbers and decimal fractions- recurring and terminating decimals.</li>
  <li>Recurring decimals: Decimals that repeat endlessly in a specific pattern. &nbsp;For example-<img src="https://imgoat.com/uploads/5b9eea6e1c/104017.png" width="245" height="45"/></li>
  <li>Terminating decimals are decimals that end: <img src="https://imgoat.com/uploads/5b9eea6e1c/104023.png" width="162" height="46"/></li>
  <li>The symbol we use for rational numbers is Q.</li>
</ul>
<h3>Irrational numbers:</h3>
<ul>
  <li>Irrational numbers cannot be written as <img src="https://imgoat.com/uploads/5b9eea6e1c/104025.png" width="30" height="44"/></li>
  <li>Irrational numbers does not fall into one of the categories above.</li>
  <li>Irrational numbers includes decimals that do not terminate or repeat.</li>
  <li>This means that if these numbers are written as a decimal , it can only be represented by a decimal that continues indefinitely .</li>
  <li>For example: &nbsp;<img src="https://imgoat.com/uploads/5b9eea6e1c/104031.png" width="279" height="66"/></li>
  <li>The symbol that represents irrational numbers is Q'</li>
</ul>
<h3>Real numbers:</h3>
<ul>
  <li>Real numbers are rational + irrational numbers.</li>
  <li>The symbol that represents real numbers is R</li>
</ul>
<p><img src="https://imgoat.com/uploads/5b9eea6e1c/104033.png" width="565" height="220"/></p>
<p><a href="https://i.pinimg.com/originals/76/d1/74/76d1749ff0c0d901d2a16d306988d345.jpg">Classification of numbers</a></p>
<p><br></p>
<p><img src="https://imgoat.com/uploads/5b9eea6e1c/104034.gif" width="589" height="100"/></p>
<p><br></p>
</html>

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