Textbook Problem

a. Place the set M = {3, 6,9, 12, 15, ...} of positive multiples of 3 in a one-to-one correspondence with the set K of all natural numbers that are not multiples of 3. Write a sentence or two that explains the general rule you used to establish the one-to-one correspondence.

b. Use your rule to determine what number from K is paired with the number 606 from M. c. Use your rule to determine what number from M is paired with the number 899 from K. In the figure below, every point on line segment AB corresponds to a real number from 0 to I and every real number from 0 to I corresponds to a point on line segment AB.

The line segment CD represents the real numbers from 0 w 2. Note that any point F on line segment AB can be paired with a unique point G on line segment CD by drawing a line from E through F. Also, any arbitrary point G on line segment CD can be paired with a unique point F on line segment AB by drawing the line EG. This geometric procedure establishes a one-to-one correspondence between the set $\left\{x\right|0\le x\le 1\}$ and the set $\left\{x\right|0\le x\le 2\}$. Thus $\left\{x\right|0\le x\le 1\}$

~ $\left\{x\right|0\le x\le 2\}$.