# basic algebra - Integers

May 29th, 2015
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The natural numbers are sometimes called whole numbers or counting numbers. There is some disagreement among mathematicians about whether or not zero should be included.[See Is 0 a Natural Number?]

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1. IntegersBefore we talk about integers, let's think about the numbers we first learned as children. Natural NumbersThe natural numbers arise from counting. We can have no objects: 0one object: 1two objects: 2... etc. :We can represent the natural numbers on a one-dimensional number line. Here is a graph of the first 4 natural numbers:We put a dot on those numbers that are included. In this case, we have graphed 0, 1, 2, and 3, but we have not included 4 to illustrate the point.We can also write the natural numbers as a set:{0, 1, 2, 3, 4, ...} The natural numbers are sometimes called whole numbers or counting numbers. There is some disagreement among mathematicians about whether or not zero should be included.[See Is 0 a Natural Number?] Less Than and Greater Than On the number line, LEFT is LESS. We use the "<" (less than) sign to indicate one number is smaller than another number. So1 < 3 We say this as "one is less than three".We use the ">" (greater than) sign to indicate one number is bigger than another.4 > 0 We say "four is greater than zero" Negative Numbers One of the biggest problems people have in mathematics is with negative numbers. Take great care with negatives!A negative number is any number whose value is less than zero. We write a minus in front of negative numbers.Examples -2-3/5-3.97-The negative numbers are represented on the left half of the number line, as follows:Once again, we have put a dot on the numbers

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