L01 - Lecture 1 Numbers, Factoring, Solving Equations and...

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Lecture 1 — Numbers, Factoring, Solving Equations and Inequalities Some sets of numbers Naturals Integers Rationals Real Numbers are “limiting values” of rationals Completeness Axiom Number line and interval notation for sets of reals
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Exponents Let a be a nonnegative real number. We make the following definitions. (1) When n is a natural number a n = (2) When a 6 = 0 a 0 = (3) When n is a natural number a 1 n = (4) When m,n are relatively prime natural numbers a m n = (5) When x is irrational a x =
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(6) When x is a positive real number and a 6 = 0 a - x = Why require a to be nonnegative to this point? A reminder for roots a 1 n : Laws of exponents: when each quantity is real, as defined at some step above, a x + y = a x - y = ( a x ) y = ( ab ) x =
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Expressions, factors, terms An expression is A factor of an expression is A term in an expression is The processes of factoring and of collecting like terms are applications of the distibutive law for real numbers a,b,c: a · ( b + c ) = a · b + a · c 3 f - 5 f = 4 a ( b + 2 a ) = 2 ω 2 + 2 ω =
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However, it is sometimes obscured: x 3 - x 2 - 6 x = s 2 3 · 2 r - s 2 · 8 r
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L01 - Lecture 1 Numbers, Factoring, Solving Equations and...

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