Monday, February 8, 2010

Learning Integers & Non Integers

What is an integer? { ... -3, -2, -1, 0, 1, 2, 3, ... }
Integers are the whole numbers, negative whole numbers, and zero. For example, 43434235, 28, 2, 0, -28, and -3030 are integers, but numbers like 1/2, 4.00032, 2.5, Pi, and -9.90 are not. We can say that an integer is in the set: {...3,-2,-1,0,1,2,3,...} (the three dots mean you keep going in both directions.)

It is often useful to think of the integers as points along a 'number line', like this:

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10_____________________________________________________

Note that zero is neither positive nor negative.

About integers
The terms even and odd only apply to integers; 2.5 is neither even nor odd. Zero, on the other hand, is even since it is 2 times some integer: it's 2 times 0. To check whether a number is odd, see whether it's one more than some even number: 7 is odd since it's one more than 6, which is even.

Another way to say this is that zero is even since it can be written in the form 2*n, where n is an integer. Odd numbers can be written in the form 2*n + 1. Again, this lets us talk about whether negative numbers are even and odd: -9 is odd since it's one more than -10, which is even.

Every positive integer can be factored into the product of prime numbers, and there's only one way to do it for every number. For instance, 280 = 2x2x2x5x7, and there's only one way to factor 280 into prime numbers.

There are also things called non integers....such as fractions,Pi, and repeating decimals.

Example Question:
y is a integer.
-3 < y < 2
what are all the possible values of y?

So it would be all the numbers in between -3 and +2
Answer: -2,-1,0,+1

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