What is NOT a real number?

Question

Please give examples of numbers which are NOT real numbers along with explanations.

Answer 1

The square root of -1 cannot be a real number, because there's no number which, when multiplied by itself, gives -1. So the square root of any negative number cannot be a real number, because for any number -n, it is equal to -1 x n. You can take the square root of the positive n, but not the -1. We call the square root of negative one by the letter "i", standing for "imaginary". The square root of -16 would be +/-4i. Zero is a real number, because it denotes the number of things when there aren't any, and it is a placeholder for the origin of a real line. Negative numbers are also real numbers, as used on a number line, or as a measure of the balance in your bank account if you go into your line of credit.

Answer 2

First, in defense of zero, let me say this. Zero is a
real number. It's sad that there's still so much prejudice
against zero. The reason that Roman Numerals are so
impractical is that they don't include a zero. Every time you
increase by a factor of 10 you need 2 new digits. What if
the Romans had a trillion dollar debt like the USA does(
thank you Mr Bush). They would need 24 unique digits.
Multiplication is nearly impossible and algebra and calculus -
totally impossible with Roman numerals because there is
no zero.
The multiplicative identity is 1. A X 1 = A, A/A=1. Similarly,
zero is the additive identity. A + 0=A, A - A=0.
In physics there is the vacuum ( zero mass) and in probability there is the null set(zero elements) and in chemistry there is
the noble gas or the stable compund(zero valence). Among people, there is the zero(no brain). Applys to people who can't
comprehend that zero is real. But I digress.

The most restrictive definitions of numbers are positive and
negative whole numbers. Notice that the word "negative" does
not imply anything depressing about a number's attitude. It's
just a way of designating which direction it is from zero(ehem).
One step less restrictive are rational and irrational numbers.
And here again these labels do not suggest anything about
the sanity or emotionality or wisdom of the numbers. It's just a way of categorizing a number as capable of being expressed
as the ratio of 2 whole numbers(other than 1 or zero(ehem))
or not.
That brings us to real and imaginary numbers. These labels
do not imply anything about existing in our dimension of reality or not. Just ask an electrician who uses imaginary numbers
all the time. It's just a way of extending the usefullness of
algebra. If you think of the number line as having one dimension
and all real numbers lie on it, then imaginary number are in
a dimension perpendicular to it. Real numbers go right and left
of zero(ehem) and imaginary numbers go up and down from
zero(ehem). The foundation of imaginary numbers is i, the
√(-1) . As with any square root, (√a)(√a)=a, so it is with i.
(i)(i)=√(-1)√(-1)=-1. The 2 axis(real and imaginary) form what
is known as the complex plane. A position on the plane is
designated a+bi where a is a number corresponding to the
horizontal position and b is a number corresponding the
vertical position. The "+" in between them does not imply
addition. It might better be represented as (a,b).
Some examples of complex numbers are (1/2 - (√3/2)i) and
(-1/2 - (√3/2)i) which are two of the three cube roots of 1.
The third one is 1 itself ofcourse.

Answer 3

A number which is not real, i.e. is "imaginary" is of the form i, 2i, 3i, etc.

i is defined as the square root of - 1. Or to put it another way, a number which, when multiplied by itself, has a product of - 1.

This doesn't work in our mathematical system, because a negative no. x a negative no.= a positive no.
A positive no. x a positive no.= a positive no.
A positive no. x a negative no.= a negative no.


That is, +2 x +2 = +4, - 2 x- 2 = +4, +2 x - 2 = - 4.

Imaginary numbers, though, follow the same rules of mathematics as real numbers.

Answer 4

First, to repeat many answers so far, the square root of -1 is denoted by the letter "i", and the square root of any negative number is some multiple of i. These are "imaginary" numbers, and they are not real, but they are only a special case.

The most general kind of not-real number is a complex number (A + Bi) where A and B are real, and "i" is the square root of -1. A is called the "real part", and Bi is called the "imaginary part", of the complex number.

Answer 5

This Site Might Help You.

RE:
What is NOT a real number?
Please give examples of numbers which are NOT real numbers along with explanations.

Answer 6

The square root of a negative number is an imaginary number.

(There's no real number which you can mulitply by itself to give a negative number.)

Answer 7

Apart from imaginary numbers, everything is real.

Answer 8

http://en.wikipedia.org/wiki/Imaginary_number


Imaginary numbers

Answer 9

Sqare root of any negative number...... i.e. squ root of -2 cannot be real. Thus the "i" or "j" (j is the engineering term) notation is used to identify a imaginary number.

Answer 10

an imaginary number which has an imaginary part with the square root of -1 as a factor.