Sets and Numbers

[Music] what is a set well this is a set [Music] and this is a [Music] set and this too is a set sometimes we call a set a group or a [Music] collection set group collection all mean the same is this a set would you call this a set the things in a set are called the members of a set or the elements of a set is this an element of this set it is an element of the set because it is one of the things in the set is this a member of this set it is not a member of the set because it is not one of the things in the set here is the set of things in Mary's lunchbox is everything in Mary's lunch box the same the elements of a set do not have to be the same what makes this set like this set there are just as many elements in this set as there are in this set we can see that there are just as many elements if we draw a line from each element of one set to an element of the other this is called one: one matching when there are just as many elements in one set as in another we say the sets have the same number and are equivalent a boat has sprung a number of leaks is the set of corks equivalent to the set of leaks by matching the sets one to one we find that the sets have the same number and are equivalent do these sets have the same number the sets do not match one: one so they do not have the same number this set has more elements than this set so they are not equivalent when the Sheep go out to the fields the farmer puts aside a pebble for each sheep there are just as many elements in the set of Pebbles as there are in the set of sheep that went out later when the Sheep come back he matches the Pebbles and the Sheep one to one to be sure there are still just as many sheep as there are Pebbles the sets do not match there are more Pebbles than sheep a sheep must be lost here he comes now the sets match one to one and are equivalent how many elements are there in this set this set has the same number of elements if you want to tell somebody how many are in each of these sets you say two if you want to show somebody how many you make this Mark the mark you make that shows how many of anything is called a numeral the farmer wants to remember how many eggs the hen has laid this morning so he writes the numeral for the number of eggs and tells his wife two and holds up two fingers now you think about two two is how many apples this many two is what number of parents this many how many circles is this here is a set with a different number of elements and other set sets with just as many the number in each of these sets is four you can write the numeral four this way how many wheels are there on a wagon how many balls are in this set how many moons do we see in the sky at night one the numeral one looks like this how many suns do we see in the sky during the day one how many trees do you see one how many balls one here is a set with a different number of elements and another set with just as many in it how many elements are there in each of these sets three elements the name for three elements is written like this how many elements are in this set how many fingers do you have on one hand you have five fingers you write the name for five like this how many elements are in this set how many elements are in this set its number is five here are all the numbers we have learned so far we haven't talked about this set yet it has no elements in it it is an empty set its number is zero how many eggs has the hen lay today she has laid zero eggs the farmer writes zero and tells his wife zero let's look at the numbers we have learned in a different way zero and one more is one and one more is two and one more is three and one more is four and one more is five zero 1 2 3 4 5 you can find the number of any set by counting its elements counting is like sneaking up on the number of a set this set has one element and one more which is two and one more which is three and one more which is four and one more more which is five and no more so the number of the set is five one 2 3 4 5 now you can see that the last number you name is always the number of the set the set that has five and one more has six elements you write six like this the little girl who owns the six dolls can keep them all and give her sister zero she can keep five and give her sister one she can keep four and give her sister two she can keep three and give her sister three she can keep two and give her sister four she can keep one and give her sister five she can keep zero and give her sister six so you see there are many different ways you can think about a number six of anything and one more is seven you can write seven like this count the elements in this set seven and one more is eight the mark for the number eight is this how do you think of the number eight like this like this like this or like this eight frogs in a pond one more frog hops in now there are nine to show how many frogs there are we write the numeral nine this way if there are nine blocks and one more then there are 10 the numeral 10 looks like this long ago people found the number of a set by matching the elements of the set one to one with their fingers one 2 3 4 5 6 7 8 9 10 we have explored how to match the elements of sets one to [Music] one how to find the number of a set by counting how to name the number you have found how to think of a number in different ways [Music] by using what we have explored here you will be able to find out how many there are of anything more than that you will be able to tell how many there are and show how many there are to anyone else so that they will know too [Music] a [Music] [Applause] [Music]