Using the listing method, write the set of integers that are greater than minus 155.
Let’s read through our problem again slowly and pick out any terms that we might not be sure of. Firstly, we’re told to use the listing method to write a set. The listing method is just a way of writing a list of the elements that are contained in a set. The list of elements sits between two braces. And each element is separated by a comma. We often use these three dots, the ellipsis mark, to show that the list continues, and so on. So let’s continue reading and find out what set we’re supposed to list.
Firstly, we can see that this is a set of integers. Integers, of course, are whole numbers. So we’re asked to write the set of whole numbers that are greater than minus 155. Notice the negative symbol there. We’re dealing with negative numbers here. So what are the numbers that are greater than minus 155? What about minus 156, minus 157, minus 158, and so on? Are these the sorts of numbers that we need to be thinking about?
Well, if we sketch a number line for a moment, we can remind ourselves that as we move from left to right on a number line, the numbers get greater. And if we’re working within negative numbers and we’re getting closer to zero, those numbers look like they’re getting smaller: minus 155, minus 154, minus 153, and so on. These numbers are actually becoming greater. They’re increasing as we get closer to zero. And so we can use our knowledge of negative numbers to write this set of integers.
To begin with, we’ll draw a brace on the left-hand side. And then let’s write the set of whole numbers greater than 155. Shall we start with minus 155? No, this number is not greater than minus 155. We need to begin with minus 154. We’ll write a comma to separate the elements. And then we’ll write the next element, which is minus 153, then minus 152, minus 151, minus 150. And let’s stop there because we could keep going on and on and on. To show that the set continues, we can draw our ellipsis marks, those three dots, and then finally draw our right-hand brace.
We’ve used the listing method to write the set of integers that are greater than minus 155. The answer is a set containing the elements minus 154, minus 153, minus 152, minus 151, minus 150, and so on.