Yesterday I finished up the Introductory Algebra Review on Udacity ( I know the certificate says 07.25.13 but that was for getting 80% of the questions right, I finished out the last unit and test on the 27th), I'm starting the College Algebra course today. Lesson one is about numbers, numbers are a construct in that they do not exist in the real world, we use the concept of numbers to do everything from balancing our checkbooks to launching satellites into orbit. Natural numbers are the numbers 1 to infinity, increasing by 1 at each step so 1, 34 and 375 are natural numbers but -3, 3.6, and 0 are not. Whole numbers are all natural numbers and the number 0. Integers are all whole numbers and negative numbers that are not fractions or decimals so they range from -infinity to +infinity. These are all sets of numbers, of course a set can be made up of any combination of numbers. Another way to express the relationship of of one set of numbers to another is to say x is a sub-set of y, for example whole numbers are a subset of integers because all whole numbers are integers. Rational numbers are any number that can be written as a/b where a and b are integers and b is not 0. Irrational numbers cannot be written as ratios of integers, so any square root that is not a perfect square is an irrational number, pi is also an irrational number.
There is also a review of variables, constants, expressions and equations. I am not going to go back over them because that information is in my previous algebra posts.