Chapter 3.5, Problem 1MS

Lining up. Can you draw a line segment that has more points than the line segment L?

L_________

To determine

Whether it is possible to draw a line segment that has more point than the given line segment L.

Answer to Problem 1MS

No, it is not possible to draw such line.

Explanation of Solution

Given information:

A line segment L is given by

  

Concept used:

One-to-one correspondence:If members of one set Xcan be evenly matched with the members of another set Y, then the situation is called One-to-one correspondence.

The word “evenly matched”tails that each member of X can be paired with one and only one member of Y, and vice versa. None of the members from either set should be left unpaired.

A line segment contains infinite number of points. Points do not have its width or length. But one can imagine a point with dot width and length.

So, no one can count the number of points on a line segment.

Hence, it is impossible to draw a line which has more points than the given line segment L.

Now, if two lines are drawn as shown below.

  

Each point on the line L has a partner on the line segment M. So, there is a -one-to-one correspondence between the points on the line segment L and M.

One-to-one correspondence between two sets are possible if and only if they have equal number of elements.