Find the set of natural numbers that are less than seven.
Remember that a set in maths is a collection of numbers or objects. And we can think of the set as representing an object by itself. We’d expect the set in this question to contain different numbers. But as a whole, we could talk about it as a set of natural numbers that are less than seven. We sometimes say that natural numbers are the numbers that we used to count with. Another definition is a nonnegative whole number. So we can’t go lower than zero, but all the whole numbers from zero onwards.
You could draw this on a number line. If we draw arrows on both ends of our number line, it shows that the numbers continue to the left into negative numbers and to the right into positive numbers. All the natural numbers are the numbers that we see to the right of and including with zero. These are all nonnegative whole numbers. So we can label our natural numbers on the number line. Zero, one, two, three, four, five, six, and seven. Of course we could continue eight, nine, and so on. But we only need to think about these particular natural numbers in this question.
We’re asked to find the set of natural numbers that are less than seven. The only two numbers on our number line that we really need to think about is, do we need to include zero. And should we include seven itself? Let’s think about zero. Is zero nonnegative? Yes, it’s not a negative number, is it? And is it a whole number? Well, it’s not a decimal. So we can consider it as a whole number. We should include zero as part of our set.
What about the number seven? This is nonnegative. And it’s a whole number. So it must be a natural number. But we were asked to find all the natural numbers that were less than seven. Could we say that seven is less than seven? No we can’t. So we can’t include seven as part of our set. Remember that when we write a set, we write it within braces. So let’s do that with our answer now as we recall the set of natural numbers that are less than seven. And we need to use commas to separate each number in the set.
The set of natural numbers that are less than seven are zero, one, two, three, four, five, and six.