what is Real number?

Question

in math

Answer 1

Real Number

Rational Numbers

Irrational Numbers

Integers

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Answer 2

A real number is the set of all rational and irrational numbers.
Of course, this means you'd have to know what rational and irrational numbers are.

Rational numbers are numbers which can be expressed in the form p/q, where q is not equal to 0 and where p and q are integers. This, of course, requires the definition of integers.

Integers are positive and negative whole numbers. But oops, we require the definition of whole numbers!

Whole numbers encompass all of the natural numbers, plus 0. Which means we would have to know what natural numbers are.

Natural numbers are {1, 2, 3, 4, .... }
Whole numbers are {0, 1, 2, 3, 4, .... }
Integers are { ... -3, -2, -1, 0, 1, 2, 3, 4, ... }
Rational numbers are { p/q, where p and q are integers and q non-zero}

It subsequently follows that all natural numbers are whole numbers, all whole numbers are integers, and all integers are rational numbers (since they can be expressed as themselves over 1).

Irrational numbers are those whose decimal neither terminate nor repeat. Examples of rational numbers are PI, sqrt(2).

The real numbers are the set of rational and irrational numbers.

Answer 3

real number is anything that's not imaginary. Real numbers are a sub-division of imaginary numbers where the imaginary form a+bi has b=0. Anything else is a real number. For example: pi, e, gamma, 1, 2, 0, cos(2.5), 500,000, infinity, are all real numbers (I'm not exactly sure on the last number).

Answer 4

All numbers be they rational or irrational are real numbers, except those involving sqrt(-1)

Answer 5

any number can be represented as (a+ib), (where i= sqrt(-1)), in an argand plane.
(argand plane is similar to two dimensional coordinate axis where any point in a plane can be specified.)
Analogus to 2 dimensional coordinate axis the two axis are real axis and imaginary axis. 'a' in (a+ib) correponds to real part and b corresponds to imaginary part.
any number whose imaginary part is zero ie b=0 is called a real number.

Answer 6

it is either a raitonal or irrational