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June 8th, 2017, 11:19 PM   #1
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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 :

$\displaystyle |x-1|<b\Longrightarrow |x^3-1|<a$
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June 9th, 2017, 01:28 AM   #2
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How are you supposed to set out a solution for the first two problems?
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June 9th, 2017, 02:03 AM   #3
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1)$\displaystyle a\geq b \land b\geq c \implies a\geq b \geq c \implies a\geq c$
2)$\displaystyle a\geq b \land b \geq a \implies a\geq b \geq a \implies a=b$
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June 9th, 2017, 03:50 AM   #4
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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?
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June 9th, 2017, 01:20 PM   #5
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Quote:
Originally Posted by Country Boy View Post
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?

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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