the (zero-factor property)
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Algebraic Properties of Real Numbers The basic algebraic properties of real numbers a,b and c are: Closure: a + b and ab are real numbers Commutative: a + b = b + a, ab = ba Associative: (a+b) + c = a + (b+c), (ab)c = a(bc) Distributive: (a+b)c = ac+bc Identity: a+0 = 0+a = a Inverse: a + (-a) = 0, a(1/a) = 1 Cancelation: If a+x=a+y, then x=y Zero-factor: a0 = 0a = 0 Negation: -(-a) = a, (-a)b= a(-b) = -(ab), (-a)(-b) = ab
x-ab=0 x=ab
Any number, raised to the power 0 is 1.This comes from the index law: ax* ay= ax+yLet y = 0 and you have ax* a0= ax+0But x+0 = x so the right hand side is ax.That means ax* a0= axSince this is true for all a, a0must be the multiplicative identity = 1.Any number, raised to the power 0 is 1.This comes from the index law: ax* ay= ax+yLet y = 0 and you have ax* a0= ax+0But x+0 = x so the right hand side is ax.That means ax* a0= axSince this is true for all a, a0must be the multiplicative identity = 1.Any number, raised to the power 0 is 1.This comes from the index law: ax* ay= ax+yLet y = 0 and you have ax* a0= ax+0But x+0 = x so the right hand side is ax.That means ax* a0= axSince this is true for all a, a0must be the multiplicative identity = 1.Any number, raised to the power 0 is 1.This comes from the index law: ax* ay= ax+yLet y = 0 and you have ax* a0= ax+0But x+0 = x so the right hand side is ax.That means ax* a0= axSince this is true for all a, a0must be the multiplicative identity = 1.
Yes
ab = 0 if and only if (a = 0 or b = 0)