Hello. I’m Professor Von Schmohawk and welcome to Why U. In the previous lecture

we saw how to define sets and their members through the use of set-builder notation. In this lecture, we will learn about several

types of relations between sets. One such relation is “equality”. If two sets contain exactly the same elements

they are said to be equal. For example, set A, which consists of

the elements one, two and three and set B consisting of

the elements two, three, and one are equal since they both contain

the same elements. Notice that it doesn’t matter that their elements

are listed in different orders. This is because the order in which the elements

of a set are listed is irrelevant. The set consisting of one, two, and three is exactly the same as the set

consisting of two, three, and one. The list does not imply that there is any

particular order to the elements. It only says that every element listed

is a member of the set. So if sets A and B contain the same elements

then they are equal. Another important relation between sets

is the relation of “subset”. If all the elements of set A

are also contained in set B then we say that set A

is a subset of set B. This relation is denoted using

the subset symbol. If two sets, A and B, are equal

then they are subsets of each other. This is because all the elements of A

are members of B and all the elements of B

are also members of A. So any two sets that are equal

are subsets of each other. And since every set is equal to itself

every set is also a subset of itself. So the subset symbol can be used whenever all the elements of A

are also members of B whether A has the same number of elements

as B or has fewer elements. But when A has fewer elements, we can be more

specific and call A a proper subset of B. We denote this using the proper subset symbol which is the subset symbol

without the line underneath. In addition to the relation of subset,

a set can also be a “superset”. In any case where set A

is a subset of set B we can also say that set B

is a superset of set A. This relation is denoted using the superset

symbol, which is the subset symbol reversed. Likewise, if A is a proper subset of B

then B is a proper superset of A. But what about the empty set,

the set containing no elements? The empty set is considered to be a subset

of every other set including itself. In fact, the empty set is the only set

which is a subset of every set. So far we have represented sets

by listing their members or using set-builder notation or by drawing little ovals

with the elements inside. In the next lecture, we will see how to

visualize sets using Venn Diagrams.

i like your revolutioninzed way of teaching….

only 2 comments and only 2500, subscribers, he deserves a lot more people. Oh yeah, only 16 likes (I just liked đ

Very useful for teaching middle school. Thanks NyWhyU đ

Very helpful, thanks!

hi .. can i download ur video … it so very helpful for student here to learn …

A very nice representation of set, subsets, and supersets! (Discrete Math-VCU).

thanks man very innovative way of teaching

woot, math…

great way to explain

on the proper subset, what If A has fewer elements than B, also A has an element that B does NOT. Would this still make A a proper subset of B?

Unbelievable these videos should have way more subscribers and views!

Can you make a video about age problems,number problem, and inequalities????….please….

03:30 And this makes a problem when we try to count the number of elements in a set: if an empty set is always a subset of every set, that means that it also needs to be counted as an element when we have a set of sets. And this is the case with the set-theoretical definition of numbers, which is based on nesting empty sets one inside another and counting them.

+quantumsingularityup not really. In order to reason about sets, you need the rules of reasoning in the first place. Therefore, logic is more basic than set theory (and perhaps the most basic in all Mathematics).

then what's the difference between equality and subset ?

That into is like powerpuff girls

Well Explained. Thanks.

However, I'm wondering about the tobacco smoking pipes.

tobacco smoking pipes!? Are you promoting tobacco !?

lol love it i love whyu

Can you make videos in Combinatorics?

This is a lot easier and more fun than being shoved into a classroom at 7:00am while people throw rubber bands and insult you across the room while the teacher corrects homework all day instead of teaching and then fail because you forget to turn in your work :).

I want to make a set of all fractions.

Can you please tell me how to say that a fraction has to be simplified in notation? (note: the fraction is one variable, not two seperate variables)

That video is fire

Why is the empty set considered to be a subset of every set? A set other than an empty set is not empty (has some number of elements), how are they even related?

Ummmm the lady has 1,48 foods she ate 1,67 how many DOSE she have leftover heheheheheh MATH ppl

Thanks for this video it solves my confusion

thnk