+129899 what does it mean when you say classify a real number?
We have two broad classes of numbers, real and non-real
The real numbers include, well, those found on the "number line"
We have several categories of "real" numbers:
1) Natural numbers....usually known as "counting numbers"....1,2,3, etc. "0" is sometimes included, too. If "0" is included, these numbers are sometimes referred to as "whole" numbers.
2) Integers....basically...all the natural numbers, "0," and the negatives of the naturals...i.e., ...-3,-2;1,0,1,2,3... These extend to infinity - both positive and negative - on the number line
3) Rational numbers - basically, anything that can be expressed as a fraction... 2/3, 4/5, etc. All the integers are rational because I can express something like "10" as 20/2 or 80/8, etc. "0" is rational, too, because I can write it as 0/1, 0/2, 0/3, etc. Also, repeating decimals are rational.
Note that all integers are rational, but not all rationals are integers !!! Thus, the "integers" form a subset of the'"rationals."
4) Irrational numbers - Any real number not capable of being expressed as a ratio. These include things like (pi), (e), etc. Any positive number that cannot be wholly taken out of a square root is also irrational. Thus, SQRT(5), 6*SQRT(3), etc., are irrational. Also, non-repeating decimals are irrational.
Non-Real numbers - You will encounter these in "upper" maths. They're known as "complex numbers" or, more familiarly, "imaginary" numbers - a poor name, because we can actually graph them on a "complex" plane!!! These include things like 3 + 6i, 4i, -5i, etc., where the "i" is the "imaginary" part. Any "negative" square root is also "imaginary" (complex).
I think I've covered most everything. Here's a website that presents a nice picture of what I've presented. It may even throw in a few "extra" things, too !!!
http://www.basic-mathematics.com/classification-of-numbers.html
