Number system has broadly been classified into two categories - Real numbers and Complex numbers.
• Complex numbers are totally out of context for GRE exam. These are the numbers with an imaginary component (iota, where i = Sq.rt(-1) with it.
e.g. Sq.rt(-2), Sq.rt(-3), Sq.rt(-4) etc .
• So, in terms of GRE syllabus, Real Numbers are the biggest set and is defined as any number which can be represented on the number line.
• Therefore, any number one can think and which is uniquely denoted on number line has to be a real number.
• Real numbers can be:
• Positive, Negative and Zero
• Rational and Irrational Numbers
• Integers and Fraction/Decimal Numbers
• Even and Odd Numbers
• Prime and Composite Numbers
• Natural and Whole Numbers
Positive, Negative and Zero:
Any number more than zero is positive, while any number less than zero is negative. Zero is neither positive nor negative.
Rational and Irrational Numbers:
Rational number: Any number which can be written in the form of P/Q; where Q should not be equal to zero.
• Rational numbers can be terminating decimal.
e.g.½= 0.5, 2/5 = 0.4, 0.12345 etc.; these terminating decimal can be written in the form of P/Q, hence
these are rational numbers.
• It can be non-terminating decimal as well, but also has to be recurring/ repeating decimal.
e.g. 1/ 3 = 0.3333. .., 2/3 = 0.6666. .. , 0.123412341234. ...; since these non-terminating decimals are
recurring decimal, so these can also be written in the form of P/Q and hence they are rational
Irrational number: Any number which cannot be written in the form of P/Q is irrational. The reason why these
can't be written in the form of P/Q is because these are strictly non-terminating and non-recurring/ nonrepeating.
e.g. n = 3.14156 .... (22/7 is a rational number and just an approximation of n)
sq.rt(2) = 1.414 ...
sq.rt(3) = 1.732 .. .
sq.rt(5) = 2 .2 36 .. .
square root of all integers except perfect square.