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Algebraic Properties of Real Numbers
The basic algebraic properties of real numbers a,b and c are:
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Closure: a + b and ab are real numbers
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Commutative: a + b = b + a, ab = ba
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Associative: (a+b) + c = a + (b+c), (ab)c = a(bc)
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Distributive: (a+b)c = ac+bc
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Identity: a+0 = 0+a = a
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Inverse: a + (-a) = 0, a(1/a) = 1
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Cancelation: If a+x=a+y, then x=y
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Zero-factor: a0 = 0a = 0
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Negation: -(-a) = a, (-a)b= a(-b) = -(ab), (-a)(-b) = ab
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