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Question 88284: How do I determine a real number, rational, irrational or natural number is? I have just returned to college and am taking college algebra. I need some basic information immediately. This is the simpliest start for me. Thank you for your assistance and I hope this is a good question. I am looking for a definition and examples of the above.
June
Answer by longjonsilver(2297)   (Show Source):
You can put this solution on YOUR website! First, the Natural numbers are the counting numbers 1,2,3,4,5,... etc. Note no negatives and usually no zero although some definitions have zero in the Natural numbers.
A larger set of numbers are the Integers - all whole numbers. Integers include the Natural numbers plus zero and all negative whole numbers.
Rational numbers are those numbers that can be written as a fraction (a/b) where a and b are integers eg 6 is rational since it can be written as 6/1 or 12/2 etc. 12.3 is rational since 12.3 is 123/10. Even repeating decimals are rational like 0.232323 recurring is 23/99.
At first glance then you would assume that every number is rational. This is not the case. There are some special numbers that never repeat themselves but go on for ever (at least we have never found the end). The classic example is 3.1415.... which is given a special name since we cannot write it: as soon as we stop writing it, that becomes an approximation. We call that irrational number, pi and its symbol is 
Similarly  is a never ending, never repeating decimal so that too is not rational --> it is irrational. Same for  . However,  is 2 which is rational. But in general, the majority of square roots are irrational.
To complete this level of maths understanding, if we have the set of rational number and all the irrationals, then this is called the Real set of numbers - basically the real set covers any eventuality for the majority of maths. Beyond Real numbers are Complex numbers but that is another story entirely.
Hope this helps
cheers
Jon
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