Problem 4. (Due September 4.) Prove
that Z3Z3 is not an ordered field.
Here is a solution for Problem
1.
The reverse (⇐⇐) implication is false.
Let X={♠️,♣️,♦️️}X={♠️,♣️,♦️️} and Y={?,?}Y={?,?}.
Define ff by f(♠️)=f(♣️)=?andf(♦️)=?..f(♠️)=f(♣️)=?andf(♦️)=?..By
checking all four possible pairs of disjoint sets from YY, it
is easy to verify the inverse images of disjoint subsets
of YY are disjoint in XX, but ff is
clearly not injective
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