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Properties of Real Numbers

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Properties of Real Numbers

Properties of Real Numbers

\text{Let }a,b,c\in\mathbb{R},\,\,\text {then:}
Property Addition Multiplication
Closure (a+b)\in\mathbb{R}\, (a\cdot b)\in\mathbb{R}\,
Commutative (a+b)=(b+a)\, (a\cdot b)=(b\cdot a)\,
Associative a+(b+c)=(a+b)+c\, a\cdot(b\cdot c)=(a\cdot b)\cdot c\,
Distributive a\cdot (b+c)=ab+ac\,
Identity a+0=a\, a\cdot 1=a\,
Inverse a+(-a)=0\, a\cdot \left (\frac {1}{a}\right )=1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\! a\neq 0
Zero a+0=a\, a\cdot 0=0\,



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