The following items give definitions of terms. Write what the definition is for the opposite of the defined term. For example, if the term is "transitive," what does it mean to NOT be transitive? These negations should be useful in the sense that they involve no double negatives and expressions are simplified as much as possible.
a) A relation on a set S is transitive provided for every a,b, and c in S, if a is related to b and b is related to c then a is related to c.
b) A set A of continuous functions on 0,1 separates points provided for any x,y in 0,1 where x!=y, there exists an f in A such that f(x)!=f(y).
6. The following items give definitions of terms. Write what the definition is for the opposite of the defined term. For example, if the term is "transitive," what does it mean to NOT be transitive? These negations should be useful in the sense that they involve no double negatives and expressions are simplified as much as possible.
a) A relation on a set S is transitive provided for every a, b, and c in S, if a is related to b and b is related to c then a is related to c.
b) A set A of continuous functions on [0,1] separates points provided for any x,y in [0,1] where x y, there exists an f in A such that f() f(y).