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Question 497707: can you name the subsets of the real numbers to which each number belongs?
3/4 -8  45,368  -2/3
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
If a number cannot be represented by the quotient of two integers, then the number is Irrational. The number isn't insane, but it cannot be represented as a ratio. 
If a number can be represented by the ratio of two integers, the number is Rational. 
The positive and negative whole numbers are the Integers. 
Non-negative whole numbers are the Natural numbers. (Actually, there are varying opinions on the exact definition of the set of Whole Numbers and the set of Natural numbers. Whole Numbers could mean Natural Numbers in the sense of positive integers, i.e.  . Or Whole Numbers could mean Natural Numbers in the sense of non-negative integers, i.e.  . Or Whole Numbers could be used to mean the entire set of Integers, i.e. )
Note that Natural numbers are a proper subset of the Integers which, in turn, is a proper subset of the Rationals.
45,368 is Natural, Whole, Integer, AND Rational.
-8 is Whole (maybe), Integer, and Rational
All fractions and explicitly stated decimals, even those that repeat forever, are Rational.
Everything else is Irational.
Any number that is the root of a non-zero polynomial function with rational coefficients is an Algebraic number. Any other number is a Trancendental number. Only one of the numbers in your list is Trancendental. Can you find it?
John
My calculator said it, I believe it, that settles it
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