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Question 345766: How are realnumber broken down
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
I assume you are asking about the subsets of the set of real numbers.
Real numbers consist of the rational numbers (those numbers that can be expressed as the quotient of two integers) and the irrational numbers (NOT the quotient of two integers)
Irrational numbers are of two kinds, algebraic and transcendental. The algebraic irrationals are roots of non-constant polynomial equations with rational coefficients, example:  . The transcendental irrationals are not roots of such equations, example: 
Rational numbers consist of integers and non-integer quotients of integers.
Integers are positive and negative whole numbers plus zero. The positive whole numbers are the Natural Numbers.
 is Natural, an Integer, Rational, and Real
 is Rational and Real
 is an Integer, Rational, and Real
 is Algebraic Irrational (one of the roots of  ) and Real
 is Transcendental Irrational (base of the natural logs) and Real
John
My calculator said it, I believe it, that settles it
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