Sets of real numbers

Question

Information on real numers

Answer 1

Real numbers consists of the sets of natural numbers (counting numbers beginning with 1), integers (all positive and negative numbers and zero), rational numbers (all numbers that can be written as a fraction using positive and/or negative integers) and irrational numbers which can be + or - as well but cannot be written as a fraction and the decimals where the number of decimal places  are infinite and  do not form a regular pattern. For example Pi is an irrational number expressed as 3.141592653...

Answer 2

The Real Numbers are ALL numbers (including counting numbers, positive and negative whole numbers, fractions, decimals roots of numbers, logarithms of numbers etc).

the only thing not included in the real numbers are the Complex (imaginary numbers).

Think of  the set of all real numbers is any number that can be found on a number line.

Answer 3

The set of real numbers have a TON of properties depending on your level of expertise. I will point out two important ones: additive and multiplicative closure. If you add two numbers x₁ + x₂ , you always get a real number x₃. You know those word problems that start like "the sum of two numbers is 55". Yeah, that's the property that allows you to write out an equation. Multiplicative closure works the same. 

If you want to geek out on this stuff, I'd check Wiki or Mathworld for more information cause there's a lot.