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Numbers: Negative Numbers
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Negative numbers are numbers that are less than zero. They are the opposite of positive numbers. For example, if a positive number indicates a bank deposit, then a negative number indicates a withdrawal of the same amount. Negative numbers are usually written by writing a negative sign in front of the number they are the opposite of. Thus the opposite of 7 is written −7. When the set of the opposites of the natural numbers is combined with the natural numbers and zero, one obtains the [I]ntegers Z (German Zahl, plural Zahlen)... written .
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To multiply a pair of numbers if both numbers have the same sign, their product is the product of their absolute values (their product is positive). If the numbers have opposite signs, their product is the opposite of the product of their absolute values (their product is negative). If one or both of the numbers is 0, the product is 0.
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The earliest fleeting reference to square roots of negative numbers occurred in the work of the mathematician and inventor Heron of Alexandria in the 1st century AD, when he considered the volume of an impossible frustum of a pyramid. They became more prominent when in the 16th century closed formulas for the roots of third and fourth degree polynomials were discovered by Italian mathematicians (see Niccolo Fontana Tartaglia, Gerolamo Cardano). It was soon realized that these formulas, even if one was only interested in real solutions, sometimes required the manipulation of square roots of negative numbers.
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Except for the section where you have to classify numbers according to type, you really won't need to be terribly familiar with this hierarchy. It's more important to know what the terms mean when you hear them. For instance, if your teacher talks about "integers", you should know that the term refers to the counting numbers, their negatives, and zero.
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[One] name for these numbers is positive numbers. These numbers are sometimes written as +1 to show that they are different from the negative numbers. But not all positive numbers are natural (for example is positive, but not natural).
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Negative Numbers