Let l be a line. A function is called a coordinate function for l if f is one-to

Question

Let l be a line. A function is called a coordinate function for l if f is one-to-one, onto, and PQ = |f(P) - f(Q)| for every . the number f(P) is the n called the coordinate of the point P. the second part of the Ruler Postulate (Axiom 3. 2. 1) essentially states that for every line l the re exists a coordinate function on l that is compatible with the way distance is measured on the line. Assume that is a coordinate function for l. Let R be defined by (-f)(P) = -f(P) for every . Prove that -f is also a coordinate function for l. Let c be a constant and let be defined by g(P) = f(P) + c for every . Prove that g is also a coordinate function for l.

Explanation / Answer

(-f)(P) = -f(P) Since F(P) is one - one and onto, -f(P) will also be and hence , (-f)(P) also,, therefore, its a cordinate function

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