Sets and Set Notation



it set is a collection of objects the objects that are in the set are called elements or members of the set okay well we're not done with a definition yet we have to question it what objects can we have in our set what kind of collections can we form can our collection have one element in it can it have two can our collection have infinitely many elements in it can our collection be empty think about these questions as we go through a few examples here you see a collection of Beatles CDs this collection forms a set what are the elements of this set well each CD is one element of the set now we often want to know how many CDs we have in our collection that's the same as asking how many elements are in our set of Beatle CDs we count them 1 2 3 4 5 6 7 8 9 10 11 12 and 13 in this set of Beatle CDs we have 13 elements you know I just thought of a question can you think of a set that has so many elements that you can't count the number of elements in it we're going to look at such a set later on in another lesson but I leave it to you to ponder about it now let's look at another example if you make a trip to your kitchen you may come across spices the spices in your kitchen form a set and if you don't have any spices in your kitchen then the set of spices that you own that are in your kitchen will be empty here we have a jar of marbles what sense can I form out of things in this picture well we can Tonk off a set of marbles inside the jar in this picture the set of marbles outside the jar in this picture the set of jars in this picture the set of lids in this picture can you form another set and what sort of questions can you ask knowing these sets how many elements are in the set or marbles outside the jar in this picture well we have one marble right here that's outside the jar so there's one element in the set of marbles outside the jar in this picture let's look at another example how many elements are in the set of tigers that you on since I don't have any tigers the set of tigers that I own is empty but I want to leave you with some advice if the set of tigers that you own has an element in it you should never bring that element to your school especially not in your math class because if that Tiger takes the bite out of the teacher then the set of chances of you getting an 8 will be empty you see how the logic holds so as you can see a set is just a way of talking about collections of things things that you see around you you can form a scent out of pencils that you have you can talk about a set of baseball cards you can form a set out of anything and your said does not even need to have any element in it what's powerful here is that using set you can represent the ideas from all around you mathematically and then work with them we're now going to be drawing these pretty pictures but we're going to have letters or variables and numbers to represent things in the real world then we're going to work with them mathematically play with them now let's first learn how we write sets using mathematics language I'm going to form a set a named aw because this is a set of the days of the week and you've probably already guessed the elements of this set they are Monday Tuesday Wednesday Thursday Friday Saturday and Sunday now notice we use braces to enclose the elements of the set and we use commas to separate the elements inside the braces also it's a convention that we use capital letters for the names of the set so this is one way of writing a set mathematically that is we list all the elements of the set inside the braces we can describe this set another way same set W can be written as set of all X such that X is a day of the week now here this X stands for elements and these : here are read such that and this last part tells us about the elements so in this case the set W will be read as W is the set of all X such that X is a day of the week well if W has X in it and X stands for its element what are these elements X is a day of the week has to be Monday Tuesday Wednesday Thursday Friday Saturday and Sunday so just another way of saying the same thing let's look at another example I'm going to name my new set N and this is a set of first five counting numbers of course you know that the counting numbers are 1 2 3 4 5 and so on so my set n which is a set of first 5 counting numbers is a set consisting of the element 1 2 3 4 & 5 now using the other notation of writing the set I will write n is the set of all X such that X is a counting number less than 6 close brace one of the benefits of this second way of writing is that sometimes you have many elements in your set and this way you can describe this the elements of the set using words and other mathematical symbols instead of having to list them all also many times we want to say that something is a part of our set that something is an element or a member of our collection how do we say that we use this symbol and this is read is an element of let's have an example since inner set n we see one is an element of our set n then we would write one is an element of n we see that six is not in our set n then we write six is not an elemental fan so we draw a slash through a sanella meant of sign also now what about empty sets how do we represent those with mathematical symbols remember at the end of examples of a set we were talking about a set of tiger's eye and I since I don't own any tigers the set of tigers that I own was empty to say that if I let T equals the set of tigers that I own then tea since I don't own any Tigers is empty you can write it like that or we have a special symbol it's zero with a slash through it and this means an empty set meaning it has no elements in it okay this ends our introduction to set in the next video we're going to learn how to combine sets

12 Replies to “Sets and Set Notation”

  1. is this supposed to interest young people in mathematics?

  2. So basically I love Math but I hate it and I love Science because of chickens that lay eggs and I feed my pet rat with a chihuahua.

  3. par x square greater then 16 base bhi batayea

  4. x greater then 4 to bataya hai

  5. you speak like stephen hawking.Is he your ideal.???

  6. Zeezinia says:

    Thanks , good work , would you please mention all the notation and its type

  7. amirah ali says:

    thanks for the help

  8. AmpedSoup says:

    i just like how the video lasts for 11:11

Leave a Comment

Your email address will not be published. Required fields are marked *