Chapter 1: Sets

Exercise

Question

Question: 3 (i)

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State whether each of the following set is finite or infinite:

(i) The set of lines which are parallel to the x-axis

Answer

1
Determine whether there is a fixed number of lines parallel to the x-axis.
Answer: It is an infinite set.
Reason: Any line parallel to the x-axis can be written in the form y = c, where c is a real{math_tip:def_real_number} number. Since there are infinitely many real values of c, there are infinitely many such lines. Therefore, the set is infinite.
Examples: y = -2, y = 0, y = 1, y = 1.5,$...$
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