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| They are addition and multiplication |
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For all real numbers a and b:
a + b is a unique real number
ab is a unique real number |
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For all real numbers a and b:
a + b = b + a
ab=hb |
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Definition
For all real numbers a,b, and c:
(a+b)+c=a+(b+c)
(ab)c=a(bc) |
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| They are reflexive, symmetric, and transitive |
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| Distributive Axiom of Multiplication with Respect to Addition |
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Definition
For all real numbers a, b, and c
a(b+c)=ab+ac and (b+c)a=ba+ca |
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| Cancellation Property of Opposites |
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Definition
For all real numbers a,
-(-a)=a
That is, the opposite -a is a. |
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|a|=a, if a is non negative;
|a|=-a, if a is negative |
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Definition
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