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Question 268924: Are there real numbers that are neither rational nor irrational? If there are, give an example. If not, tell how you know that they do not exist.
Answer by CharlesG2(834)   (Show Source):
You can put this solution on YOUR website! Are there real numbers that are neither rational nor irrational? If there are, give an example. If not, tell how you know that they do not exist.
real number --> set of both the rational numbers (-3/4,-1,2,6/8) and the irrational numbers ( sqrt(2), pi, e )
rational number --> set of numbers that can be written as the quotient of 2 integers
irrational number --> numbers that can not be written as the quotient of 2 integers
complex number --> a+bi where a and b are real numbers and i is defined as the square root of -1, a complex number has a real part and an imaginary part so it is neither rational nor irrational
so there can not be a real number that is neither rational nor irrational
there can be a number though that is neither rational nor irrational and that would be the set of complex numbers
an example: sqrt(-81) = sqrt(9 * 9 * -1) = 9*sqrt(-1) = 9i = 0 + 9i
(0 is the real part and 9i is the imaginary part)
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