Algebraic Operations by Edu Pristine

Author of lecture Algebraic Operations

Edu Pristine

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Excerpts from the accompanying material

... - Equations and inequalities - Functions and graphs ...

... Operations "Sequence and Series" "Exponential and logarithms" "Equations and inequalities" ...

... defines that set of rules to be followed while performing the mathematical operati ons. E.g. Algebra of logic gates has ...

... Types of numbers  Natural numbers, N = {1, 2, 3, 4, 5 &..}, labeled N - Whole Numbers, 0 in addition to the Natural numbers - Integers, Z = { &.-3, -2, -1, 0, 1, 2, 3 &.}, labeled Z - Rational numbers (fractions), Q = {1/2,1/4, 4}, labeled Q  Real, labeled R Consists of ...

... we move from right to left, i.e. 16/4/3 we get 4/3 which is not correct. Evaluate (4x+3) 2 + 20/(2x+1) when X =2. First we evaluate the expression inside the brackets: 11 2 + 20/( 5) . Then we evaluate the indices. i.e 11 2 =121, we get 121+(20/5). After indices, division (20/5). Finally we get 121 + 4 =125 ...

... Commutation of addition: a + b = b + a  Example: 11+3 = 14 and 3+11=14 - Association of addition: a + (b + c) = (a + b) + c  Example 12+(4+3) = 12+7=19 and (12+4)+3 = 16+3 = 19 ...

... Example 12*(4*3) = 12*12 = 144 , (12*4) *3 = 48*3 = 144 " Existence of 1 i.e. a * 1 = a " Existence of inverses a * a 1 = 1 (but not in Z) " Distributive of multiplication a *( b + c) = (a * b) + (a * c)  Example 12*(4+3) = 12*7 = 84, (12*4)+(12*3) = 48+36 = ...