Introduction to Algebraic Inequalities[Symbols and Properties]
Inequality is simply a system of ordering, in mathematics, ordering is very important as it allows us to quantitfy numbers.
Symbols Used to denote Inequalities.
"<" Means Less than.
">" Means Greater than.
"$\leq$" Means Less than or equal to.
"$\geq$" Means greater than or equal to.
Properties of Inequalities
For $a,b\in\mathbb{R}$ then the following relations holds:
If
1. $a<b$ then $b-a>0$
2. $a<b$ then $a+c<b+c$
3. $a>b$ then $a+c>b+c$
4. $a>0$ and $b>0$ then $a+b>0$
5. $a>0$ and $b>0$ then $a.b>0$
6. $a<b$ then $ac<bc$ and $\frac{a}{c}<\frac{b}{c}$ if $c>0$
7. $a<b$ then $ac>bc$ and $\frac{a}{c}>\frac{b}{c}$ if $c<0$
8. $a<b$ and $b<c$ then $a<c$
9. $a<c{\exists}c:a<c<b$
10.$a$ is given then we can find some $b$ and $c$ such that $b<a<c$
Inequality is simply a system of ordering, in mathematics, ordering is very important as it allows us to quantitfy numbers.
Symbols Used to denote Inequalities.
"<" Means Less than.
">" Means Greater than.
"$\leq$" Means Less than or equal to.
"$\geq$" Means greater than or equal to.
Properties of Inequalities
For $a,b\in\mathbb{R}$ then the following relations holds:
If
1. $a<b$ then $b-a>0$
2. $a<b$ then $a+c<b+c$
3. $a>b$ then $a+c>b+c$
4. $a>0$ and $b>0$ then $a+b>0$
5. $a>0$ and $b>0$ then $a.b>0$
6. $a<b$ then $ac<bc$ and $\frac{a}{c}<\frac{b}{c}$ if $c>0$
7. $a<b$ then $ac>bc$ and $\frac{a}{c}>\frac{b}{c}$ if $c<0$
8. $a<b$ and $b<c$ then $a<c$
9. $a<c{\exists}c:a<c<b$
10.$a$ is given then we can find some $b$ and $c$ such that $b<a<c$
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