
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
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June 8th, 2017, 11:19 PM  #1 
Senior Member Joined: Apr 2010 Posts: 451 Thanks: 1  inequality
Can somebody give me a complete solution to the following problems: 1) $\displaystyle a\geq b\wedge b\geq c\Longrightarrow a\geq c $ 2) $\displaystyle a\geq b\wedge b\geq a\Longrightarrow a=b$ 3) given a>0 find b>0 such that : $\displaystyle x1<b\Longrightarrow x^31<a$ 
June 9th, 2017, 01:28 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,059 Thanks: 1396 
How are you supposed to set out a solution for the first two problems?

June 9th, 2017, 02:03 AM  #3 
Senior Member Joined: Dec 2015 From: Earth Posts: 157 Thanks: 21 
1)$\displaystyle a\geq b \land b\geq c \implies a\geq b \geq c \implies a\geq c$ 2)$\displaystyle a\geq b \land b \geq a \implies a\geq b \geq a \implies a=b$ 
June 9th, 2017, 03:50 AM  #4 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,734 Thanks: 707 
What "properties" of "greater than" do you know? For example, are you allowed to use the fact that "greater than" is transitive: that if a> b and b> c then a> c? What do you know? What definition of "" are you using? 
June 9th, 2017, 01:20 PM  #5  
Senior Member Joined: Apr 2010 Posts: 451 Thanks: 1  Quote:
axioms: 1) trichotomy law for ">" 2) a>b and b>c => a>c 3) a>b => a+c>b+c 4) a>b and c>0 => ac>bc Definitions: $\displaystyle a\geq b \Longleftrightarrow a>b \vee a=b$  

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