Mathematics with Prof. S.R. Naidu

Zero Zero may be defined for the present,as the absence of any magnitude.It is obtained by subtracting a number from another which is exactly equal to itself.4-4=0. IMPORTANT PROPERTIES OF ZERO  1. 0+0 =0 ;  x+ 0 =x ; -x+0= -x 2.0-0=0 ; x-0=x ; -x-0=-x we understand that x+ 0 = x- 0 ∴ +0 = - 0 3. 0 x 0 = 0 ; x x 0= 0 ; 0 x x = 0 . 4 . 0➗ x = 0 5. x➗ 0 is infinite when xキ0 ( i.e. x is not equal to zero ) and 0 ➗ 0 is an indeterminate result. 6. 0 square = 0 x 0 =0  Thus zero raised to any power is equal to zero and consequently any root of zero is equal to zero. integral numbers divisible by 2 are called even numbers integral numbers not divisible by 2 are called odd numbers in working examples the positive root is usually taken.

POSITIVE AND NEGATIVE NUMBERS When no sign precedes a term,the sign + is always understood. The use of the signs + and - is so constant and so important .The magnitude of a quantity considered apart from its sign is called its absolute magnitude.Thus a gain of Rs 5 and a loss of Rs 5 ,are equal in magnitude though opposite in sign. Addition: If two positive numbers are added together the sum is positive and if two negative numbers are added together the sum is negative ,but if a positive number and a negative number are added together the result will be positive or negative according as the positive or negative number has greater numerical absolute value. +4+ (+3)=+7 +7+ (-4)=+3 5+ (-8)= -3 (-3) + (-4) = -7 In adding up numbers it is immaterial in what order we take them,provided that each number has its own sign placed before it. Subtraction: To subtract a positive number means to add the corresponding negative number and if the number to be subtracted is negative,change it into a pos...