Negative Numbers Explained in 5 Minutes
Most people feel comfortable with zero and the positive integers..
{0,1,2,3,4,..}
So why do we need more numbers? In particular, why do we need negative numbers? The story of negative numbers reveals one of the most profound ideas in mathematics. It's an idea that shows the amazing power of mathematical thinking.
Here's the scoop..
Mathematicians love equations, but they soon realized that even very simple equations cannot be solved if all you have are the numbers {0,1,2,3,4,..}.
For example, the simple equation x+5=0 has no solution. What to do? Mathematicians took an amazing step, they invented new numbers to solve this class of equations! These are the negative numbers. So the equation x+5=0 is solved by a new number called "negative 5" or "minus 5" and written as -5. So x=-5 is the solution to the equation.
Every number n has a negative partner -n such that -n+n=0. Think of -n as the "anti-number" of n, so now the set of numbers has been extended to..
{..,-3,-2,-1,0,1,2,3,..}
This idea is profound and shows the ease with which things can be invented in mathematics.
The new number set {..,-3,-2,-1,0,1,2,3,..} is wonderfully symmetric. Imagine the numbers in a line with a mirror inserted at the 0 position. Then -1 is the mirror image of 1 and -2 is the mirror image of 2 etc.
So do negative numbers "really exist". Yes they do. In mathematics you can define new objects anytime you want!
Let's suppose that one morning before breakfast you dream up some new mathematical objects. And you also dream up an operation you can do with the objects. And your new stuff does not lead to any crazy contradictions with existing math. Then what have you done? You've invented new mathematics.
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Content written and posted by Ken Abbott abbottsystems@gmail.com
Internet Marketing Consultant