hi I'm miss Hearne let's get started in this video we're gonna talk about when sets are finite or infinite you might already be familiar with these terms I mean finite means that the set doesn't go on forever and infinite means it does go on forever but to formally define them is a little bit less straightforward so let's take a look in order to define them we're going to have to know the term whole number the whole numbers are the numbers 0 1 2 3 4 5 and so on ironically the whole numbers are an infinite set it goes on forever following a pattern of increasing by one and we're going to use the idea of the whole numbers to define finite a set is finite means that the number of elements in the set is actually a whole number if we can count the number of elements in a set and we can get a whole number a number out of the set of whole numbers then we call it finite otherwise if there's no particular whole number that gives a number of elements in the set then we call it infinite so to really get into what that means we're gonna look at some examples of some sets let's look at set a set a is a set containing the elements 2 4 & 6 now if I asked you is that a finite set you'd probably say yes because it doesn't continue on forever but another way to think about it is is there a certain whole number that is associated or that gives the number of elements in the set a and the answer to that question is yes we can count the elements in a and we can see that there are three of them since we can say that the number of elements in a is three also called the cardinality of a and since 3 is a whole number this fits our definition of what it means to be finite now let's look at set B so set B is a very special set known as the empty set it can also be represented as circle with a line through it and so how many elements do AC and B well there are none right so there are zero elements in B and we can write that as the cardinality of be the number of elements and B is equal to zero is zero a whole number yes so since we can give the number of elements in B as a whole number this fits our definition of finite how about set C so set C has something called a lip season at the three dots that indicates a pattern continues and sometimes people think that if we have that then it's automatically an infinite set but in fact if there is a beginning number and an ending number then those ellipses are not necessarily indicating an infinite set probably not so in this case we would have what let's let's write it out this is two four six the pattern is that they're increasing the elements of the set are increasing by two each time so the next number would be eight and then the next number would be ten let's count how many elements are in the set C we can see that there are five elements in the set C or in other words we could say that the cardinality of the set C is exactly the whole number 5 so that fits our definition again of being finite now let's look at set D the set D is 2 4 6 and so on with no end so if I were to try to list out the elements of the set D I would never stop so intuitively you probably realize that this is an infinite set it just keeps going there is no largest element even if I listed it out to a million there would still be another element a million and two in this set and it would continue after that as well is there a whole number that we can associate with the number of elements in this set no because no matter how many I find I can always find one more set D is what we call an infinite set so in your homework if you're one of my students you're you might see something like this and your mylabs identify the following set as finite or infinite and we're told that the set is the set of all X such that X is a natural number greater than 60 the natural numbers by the way are the numbers 1 2 3 4 and so on they're also known as the counting numbers they can be represented with a bold N and we're talking about the natural numbers greater than 60 so in this case we would be talking about the set that starts with 61 and then 62 and then 63 and so on notice it doesn't give us an ending value it goes on forever so intuitively you probably realize that this is an infinite set but in my lab they want us to explain why so what we need to do is to select the reason why so we have two options here for infinite and you can see that the set is infinite because the number of elements in the set is not a whole number fits our definition of what it means to be infinite I hope you found this video helpful if you did please remember to give it a thumbs up that helps other students to find the video you can also subscribe to miss Hearne mathematics for more math video