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Need a logical proof of [(c>0) and (|a|<c)] implies [(-c<a) and (a<c)]
I need a logical proof of the elementary statement about real numbers using order and field axioms
$((c>0)\wedge(|a|<c))\Rightarrow((-c<a)\wedge(a<c))$
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$a > b+1 \Rightarrow a>x>b$?
If I have $a,b \in \mathbb R$ such that $$a > b+1 $$
It is assured that $\exists\space x \in \mathbb Z: a>x>b$
Does this property have some special name?
How can this be proved?
This idea ...
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Possible book correction or am I missing something?
Hi I am teaching myself analysis and bought "Analysis - With an introduction to Proof" by Steven R. Lay. Now one of the practice problems is "Determine the truth value of each statement, assuming x, y ...
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