Question

Only one of the following three descriptions can be realized. Provide an example that illustrates the viable description and explain why the other two cannot exist: (i) A countable set contained in 0, 1 with no limit points.

a. True
b. False

Answer 1

The statement (i) A countable set contained in 0, 1 with no limit points is False. An example to illustrate this is the set of rational numbers between 0 and 1, which has limit points.

Step-by-step explanation:

The statement (i) A countable set contained in 0, 1 with no limit points is False. Here's an example to illustrate why:

Consider the set of rational numbers between 0 and 1. This set is countable because it can be put into a one-to-one correspondence with the set of natural numbers. However, it does have limit points. For example, the number 1/√2 is a limit point as it is the limit of a sequence of rational numbers that approaches it.

Therefore, the viable description would be (ii) A countable set contained in 0, 1 with limit points.