Properties of Real Numbers - Maple Programming Help

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Properties of Real Numbers

Main Concept

Any real numbers  and $c$ have the following properties:

 1 They are closed under addition: $a+b$ is a real number
 2 They are closed under multiplication: $a\cdot b$ is a real number
 3 Addition is associative: $a+\left(b+c\right)=\left(a+b\right)+c$
 4 Multiplication is associative: $a\cdot \left(b\cdot c\right)=\left(a\cdot b\right)\cdot c$
 5 Addition is commutative: $a+b=b+a$
 6 Multiplication is commutative: $a\cdot b=b\cdot a$
 7 They are distributive: $a\cdot \left(b+c\right)=a\cdot b+a\cdot c$
 8 0 is the additive identity: $a+0=a$
 9 1 is the multiplicative identity: $a\cdot 1=a$
 10 Each number has an additive inverse: $a+\left(-a\right)=0$
 11 Each number except for 0 has a multiplicative inverse: $a\cdot {a}^{-1}=1$

Use the sliders to choose $a$, $b$ and $c$. Use the radio buttons to demonstrate the distributive property: $a\mathit{\cdot }\left(b\mathit{+}c\right)\mathit{=}a\mathit{\cdot }b\mathit{+}a\mathit{\cdot }c$.

b=

c=

a=

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