## Tuesday, February 3, 2009

### PREP FOR GMAT: NUMBERSYSTEM

Natural Numbers: N

In mathematics, a natural number (also called counting number) means an element of the set {1, 2, 3, ...} .

Whole Numbers: W

When all the natural numbers and zero are put together, we get a new set of whole numbers. The set of whole numbers is denoted by “W”.
Hence W={0,1,2,3,4………}.

Integers: Z

The integers are natural numbers including 0 (0, 1, 2, 3, ...) and their negatives (0, -1, -2, -3, ...). They are numbers that can be written without a fractional or decimal component, and fall within the set {... -2, -1, 0, 1, 2, ...}.
Note : Decimal numbers are not integers.Example: 1.6 and 1½ are not integers.

Rational Numbers: Q

A rational number is a number of the form a/b. Where a and b are integers, b is non-zero.
Note: All whole numbers are rational numbers because they can be expressed as themselves over 1, i.e. 5 = 5/1, 0 = 0/1
Example: {2/3, 4/7,7/9……..}

Irrational Numbers: J

An irrational number is any real number that is not a rational number — that is, it is a number which cannot be expressed as a fraction a/b, where a and b are integers, with b non-zero. Informally, this means numbers that cannot be represented as simple fractions.

Real numbers R: The set of all rational and irrational numbers.

Imaginary Numbers : I

Numbers that when squared give a negative result. If you square a real number you always get a positive, or zero, result. For example 2×2=4, and (-2)×(-2)=4 also, so "imaginary" numbers can seem impossible, but they exist.
Its symbol is i or j.
i^2 = -1

Complex Numbers: C

A combination of a real and an imaginary number in the form a + bi, where a and b are real, and i is imaginary.
The values a and b can be zero, so the set of real numbers and the set of imaginary numbers are subsets of the set of complex numbers.
Examples: 1 + i, 2 - 6i