So how to use the greatest integer function. Hi I'm Jimmy Chang, I've been teaching college mathematics for nine years. And the greatest integer function from the outset seems a little intimidating, but once you understand the definition behind it, it's actually pretty easy to apply. So here we go with the definition first. Now the greatest integer function is a function of which you're looking for the greatest integer less than or equal to X. Now again, what is an integer? Think about positive and negative whole numbers, including zero. But the emphasis in on whole, because we are working with whole numbers both positive and negative. So here's a couple of really quick examples. Notice the notation though is a combination of using brackets and what looks like absent value bars, but that's a notation for greatest integer function. So for example, suppose you want to find out the greatest integer of two point one. What you want to think about is what is the greatest integer, well in other words what is the greatest whole number less than or equal to two point one. Well, that answer would be two. Now what about the greatest integer of four, in other words what is the greatest integer less than or equal to four. Well since four itself is an integer, the greatest integer less than or equal to four is going to give you four. So if there is already an integer in there, the greatest integer is just what's inside. But if they give it to you in a decimal form, then you have to think about the number that's less than or equal to. In other words, the integer that's less than or equal to the number on the inside. The only thing that is a little bit tricky is if you have negative numbers here. Now suppose you have the greatest integer of negative two point three. You want to think about the greatest integer less than or equal to two point three. Now you might think it's going to be negative two, but the thing is the definition is you're looking for the greatest integer less than or equal to X. If you think about negative two though, negative two is actually larger than negative two point three, you're looking for the greatest whole number that's less than or equal to negative two point three. Negative two is actually too large, so you have to go with negative three. Because that is the greatest integer less than or equal to negative two point three. So with negative numbers it can be really tricky. But with positives and zero it's pretty straight forward. So I'm Jimmy Chang, and that is how you use the greatest integer function.
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