Properties of Real Numbers

**Properties of Real Numbers**

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

Usage