What is the Cardinality of a Set? | Set Theory, Empty Set
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- เผยแพร่เมื่อ 20 ก.ย. 2024
- What is the cardinality of a set? In this video we go over just that, defining cardinality with examples both easy and hard. To find the cardinality of a set, you need only to count the elements in the set. The cardinality of the empty set is 0, the cardinality of the set A = {0, 1, 2} is 3. The cardinality of a set A is written |A|.
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I hope you find this video helpful, and be sure to ask any questions down in the comments!
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I should also add that for an infinite set, we say its cardinality is infinite! However, not all infinite sets are the same size. That is, all infinite sets have infinite cardinality, but not necessarily the same size infinity. That is a can of worms for a different lesson. By the way, if you want to bump some tunes - check out my math rap channel! th-cam.com/video/iwm9XGrshdU/w-d-xo.html
ExCUS meee SIR- is this the same way i give the universal set? :D))
I have learnt more in the first 45 seconds than I did in the ~33 minutes of my teacher trying to explain this simple concept. Thanks.
So glad it helped! Thanks for watching and let me know if you ever have any questions!
SAME! lol
nice same
Thank your for this video! Now I learned this lesson more enough and now i have something to do at my Exam Tommorow.
You're very welcome! Thanks for watching and good luck on the exam!
Omfg this is why I like php because it allows the use of objects. Math is my new love.
we reached 2022 and until now no one knows why the teachers in TH-cam wayyyy better than the university , this teacher is an example with cadinality one pencell
Thanks for watching, so glad to help!
Bro, You are awesome, I mean it. Why do teachers make them so difficult for students at universities?
Thank you for the clear explanations.
You're such a wonderful teacher. I like you how your instruction is clear and easy to follow. In fact ,in less than 4 minutes you make me feel Luke i could actually get math. That's so weird ( in a good way ofcourse). Thank you!
Thanks so much! I am glad it helped!
Thank you for your help sir .
I just wanted to know what the bar thing is called but now I both know and understand what is cardinality of set.😊
So glad it helped! Thanks for watching! Perhaps you already knew what the bars meant around a number, it's the absolute value. Like |-3| = 3. We also call that the magnitude, it's a number's distance from 0. So, as you saw, the bars around a set are also a sort of measure of the "magnitude" of a set, since they measure the number of elements the set contains!
One of my favorite videos in TH-cam
Thank you!
Thank you for these videos! I totally understand the way you teach. - Tina
Thanks for watching, Tina! I am glad my lessons have been helpful for you!
i was struggling with this.
Let A={a,b,c,d, e} and B = {d,e,f,g,h,i}.
The cardinality of the set |BxA\AxB| is:
thought it was 30 but its 26 but dont know how
can u answer these questions please?
Write the cardinality of each set.
M = m is a month
S = {Word, Excel, PowerPoint, Publisher}
N = {10, 15, 20, 25, 30, 35, 40, 45, 50}
C = c is a continent
R = r is a prime number less than 23
Thanks for watching, and I just released this lesson which goes over a handful of sets similar to the ones you gave. Hope it helps and let me know if you have any more questions! th-cam.com/video/KmHMot3OIQs/w-d-xo.html
Thanks this helped a lot. Simple and straight to the point.
Glad it helped! You're welcome and thanks for watching!
thanks for the great and clear video. I always though that empty set is part of every set, meaning every set would have cardinality of element + 1 (empty set)?
please what would be the cardinality of the sets {7,8) thats the close and open set
You're like a personal tutor!
Thanks for watching! Let me know if you ever have any questions!
Two finite sets A and B are such that the total number of subsets of A is 56 more than the total number of subsets of B. What are the cardinalities of A and B respectively?
I had no clue how to do this in my college math class.....thank you
So glad it helped, thanks for watching! My set theory playlist is bit of a mess, but it has many more set theory lessons you may find helpful. th-cam.com/play/PLztBpqftvzxWUF1psif8R7aUph4tsIuNw.html
Hi, I am just wondering if there is something like A = {a,a,b,c} where elements are overlapped. Will its |A| still be 4?
set contains only unique items
@@rajiabraham7884 Thanks a lot :)
@@islomkhujaakhrorov6668 Thank you sm!
I love the way that you get to the point! Subscribed!
Thanks John, glad you're finding the lessons valuable!
Thx for the vid, gotta say teachers should teach the way you do
From a diff video, it said the empty set in a set is not an empty set but a greek letter, an element. Do you agree? When you say it in english, is that how you're supposed to say it? set {1,2}, 3, and empty set are the elements of set B
What is the cardinality and subset of Y={a,e,i} ??? Sir?
yeah maybe 1 year ago will do
Amazing i understand all the concepts nearly in 1 minute keep going ! btw can you tell me outro song name ?
Nice, I hope I see more of your videos covering many topics.
There will be many more videos on many more advanced topics! Let me know if there is anything you would like to see.
Very clear sir. Thank you 😊
Glad it was clear! You’re welcome and thanks for watching!
I was bad at math but i needed to learn as i get older that's why this helped me thank you!
So glad it helped, and you'll keep getting better if you keep studying and practicing math, thanks for watching!
What should we do in terms of repeated numbers. We count 1 or 2??
Do you mean to ask how repeated elements impact the cardinality of a set? They do not. So, if A = { 1, 1, 2, 2, 2, 3 }, then |A| = 3, and everybody aside from one who is writing a question specifically to clarify this issue would write the set as A = { 1, 2, 3 }. Hope that helps!
If the empty set is an element of every set, then technically |A| = 5, or do these operations only apply to sets that have been explicitly defined? If so, it would make it tricky to validate based on set theory, because validation would only apply to a subset of subset theory.
The empty set is a subset of every set. {1, 2} is a subset of S = {1, 2, 3} but not an element thereof. 1, 2 and 3 are elements of S.
Thanks a lot for your excellent video!!
Glad to help!
Thanks sir 😊
Glad to help!
Sir I have a question. If there is a repetition in a set then
1. Can we say that it is a set ?
2. If yes than what will be the Cardinality of the set?
For example the set is { e, l, e, v, e, n}
Thanks for watching and good question! It depends what you mean by "there is repetition". If I want to capture that repetition, then a set cannot accomplish that, but there is nothing wrong with letting { e, l, e, v, e, n } be a set. But, as a set, the repetition doesn't matter, so { e, l, e, v, e, n } = { e, l, v, n }. Here is a video on cardinality with repeated elements: th-cam.com/video/1ozscvLm5uk/w-d-xo.html
Thank u sooo much 💐👍💜
Glad to help!
by the way what happen when a set has a a squared or cubed does it count as a part of the cardinality {3,6^2,}
Thanks for watching and for the question, I’m not sure what the “it” is in your sentence. The exponent is not an element, the expression 6^2, or more simply the number 36, is an element. The set {3, 6^2, 36} has two elements, for example.
thanks a lot sir. I actually not able to understand its meaning in google. but when i got to this video I m able to understand clearly. Actually I am preparing for exam...….
You're very welcome and I am glad it helped! Good luck on the exam!
Thank you so much❤
Omg thank youuu😭❤️. I'm learning math now
(cause i think math is not that hard🙂)
Thank you very much it was very helpful🙏👍
I have a question.you said the cardinality of |∅| = 0,
thats mean you didn't count ∅ as a distinct element.But while finding,
B={{1,2},3,∅}
|B|=3
You count ∅ as a element.
Why?
🤯
1:45
The difference is ∅ contains nothing, so its cardinality is 0. It is a set, but it contains nothing. On the other hand, the set B you describe contains ∅, which is indeed an additional element. Remember that ∅ is not nothing, it just contains nothing.
for every relationship what are the 4 possible sets of minimum cardiologists?
thanks
My pleasure!
I just gotta say math is so interesting!
Thanks so much for watching, I agree! Let me know if you ever have any questions!
Thank you you are a good teacher
You're welcome and thanks for watching!
I'm good at sets but I don't know what happened to me. Thanks for posting this btw😁
Then do this "GIVEN THAT P= {A,B,C,D} HOW MANY SUBSETS IN TWO ELEMENTS ONLY?"
bet that
Thank you
Thankyou sir for explaining but what if the number is repeated? it is already counted as one? or they will be counted separately?
Thankyou for answer Sir
I still do not understand this. In your second example; the answer is 3 because of the number 3 in the set or is it because you counted {1,2}, and 3 as simple elements in the set?
Thanks for watching and for the question! The cardinality, |B| is simply the number of elements in the set. In the set B there are three elements. The first element written is the set {1, 2}, the second element written is the number 3, and the third element written is the empty set { }.
We wrote the set out in what is called "roster form", which just means we have listed out the elements of the set. When we write a set like this, the primary obstacle to finding the cardinality is being able to identify what the individual elements are. I made a video focused on that challenge here: th-cam.com/video/eltZlBtWhd4/w-d-xo.html
Thx man I really understand this video cause now its time for me to answer my assignments and I'll give you a subscribe for helping me to understand Cardinalities.
So glad it helped! Thanks for watching!
I know im pretty pretty late to this but what is the cardinality of counting numbers from 5 to 25?
Thank you for this video this video gives me an idea to answer my math hehe
Thanks for the video it really help me
Glad to hear it! Thanks a lot for watching!
Thanks a lot !
My pleasure, thanks for watching!
i'm litteraly the worst Math Studebt ever :( but this helped *cOugHs* (saved) me from my homework💞
Grade Seven Problems Pa More LeL Sa Mga Tanga Dyan Katulad Ko😤
Really it helps me☺️
Glad to hear it! Thank you for watching and let me know if you have any lesson requests!
THANKS!
My pleasure, thanks for watching!
what is the cardinality of the set for {0, 1, 2, {3, 4, 5, ...}}
I cant figure it out
Great question! Cardinalities can get very tricky once we start putting sets inside of sets, as in the example you showed. So let’s look at it. We will call your set A. So, A = {0, 1, 2, {3, 4, 5, ...}}. Remember the cardinality of the set is just the number of elements in the set, and an element can be anything, it could be a number, a set, a function, or even a food, to take a less mathy example. Sets can contain anything. The key to counting the elements, really, is keeping track of commas, and what each comma means. So if we look at the set A, first we see 0, 1, and 2. Each one is separated by a comma, and these are just numbers, so each one is an element. That gets us up to 3 elements. Then, we see the ‘{‘ symbol, which means a set is being opened within the set A, we will call this inner set B. Now we know that every comma we see is actually separating elements inside of the set B, until we see the ‘}’ symbol, meaning the set has been closed. So we see ‘3, 4, 5, ...’ but all of these commas are after the ‘{‘ symbol and before the ‘}’ symbol, so we know they are not separating elements of A, they are separating elements of B. Elements of B are not elements of A. The set B is an element of A, but the things inside of B are not elements of A. Thus, we have one more element in our set A, and that element is the set B. Thus, there are 4 elements in A. The number 0, the number 1, the number 2, and the set {3, 4, 5, ...}, which we referred to as B.
Something I used to do with these problems was use color-coded commas. I think that helps illuminate the concepts a bit. Use one color to separate elements of A, but as soon as you open another set in A, or anything else that uses commas (like ordered pairs, for example), use a different color for the commas. Once the new thing you opened up closes, go back to the comma color for A. That way all elements of A are separated by a comma that is green for example, and all other objects are separated by red commas. Then, the number of elements of A would just be one more than the number of green commas (because the last element of A will not get a green comma after it, but all other elements of A will).
Let’s quickly look at a messier example. Consider the set S = {0, { }, { 1, {2, 3, {6}, 3}, { }, 6, dog, {2, 3}}, (1, 6), 78}. I think you’ll agree that S is a very ugly set. Try to find the cardinality of S before reading on in this comment. They don’t really get this ugly in any experience I have had, so if you can understand this example, even if you do not get it on your first try, you’re in a pretty good spot. Let’s look at the solution.
Recall that S = {0, { }, { 1, {2, 3, {6}, 3}, { }, 6, dog, {2, 3}}, (1, 6), 78}. Let’s count up the elements. First we see 0. That is an object, and counts as our first element. Then a set is opened up, but before any elements of that set are listed, the set is closed, so it was just the empty set. So the empty set is our second element. Then another set opens up.
Here is a good way to deal with this messy set that just opened up. Every time you see an open symbol like ‘{‘, ‘[‘, or ‘(‘, add 1 to an ongoing count in your head. Every time you see a close symbol like ‘}’, ‘]’, or ‘)’, subtract one from that ongoing count in your head. When your count hits 0, the object that was first opened has now been closed, and you can then add one to your element tally. So let’s try it. Remember we just added the empty set to our element count, so we are at two elements, and then this other set opened up, so now we have 1 in the ongoing count in our head of these open and close symbols. After the first open set symbol, we see a 1 and then another open set symbol, so we add 1 to our count and get 2. Then we see 2 and 3, and then yet another open set symbol, so again we add one to our count and get 3. Then there is a 6 and then a close set symbol, so we take one from our count and get 2. Then we see a 3 and then another close set symbol. So we take one from our count and get 1. Then we have an open set symbol, so our count goes to 2, then a close set symbol, so our count goes back to 1. Then we have the number 6, then the word ‘dog’, then another open set symbol, so we add one to our count and get 2. Then we see a 2, a 3, and then a close set symbol so our count goes down to 1, then another close set symbol sending our count finally, to 0. Thus, the set has finally been closed, and we can add one to our element tally, putting it at 3. Our elements so far are 0, the empty set, and this nasty set we just looked at: { 1, {2, 3, {6}, 3}, { }, 6, dog, {2, 3}}.
Moving on we see the ordered pair (1, 6). That adds one to our element tally, putting it at 4. Then we see the number 78, putting our element tally at 5. Then the set is closed, so that is it! The set S has a cardinality of 5. I hope that helps and please let me know if you need clarification on any of what I said in this comment, I know it is not the easiest stuff to understand through a TH-cam comment with just plain text.
4
Thank you so much💕as an 12 year old Math is not that easy...Thank you so much for this:)
You're very welcome and I am glad it helped! Thanks for watching and let me know if you have any questions!
I have a question, What if set A=(C,A,R,D,I,N,A,L,I,T,Y) n(A)=9?
cause u count the ones that are more than one letters is just 1 element right?
Thanks for watching and you're exactly right!
Hi my name is Feanne and I don't know how to do make same homework and I don't know the answer of this direction
Hi Feanne, thanks for watching! I'd love to help but I'm not sure what your question is! If you have a question could you try rephrasing it?
@@WrathofMath sir i have a homework and i actually dont understand it and that queston is set M is the set of months in a year"
Sir please tell what will be the cardinality of B ={phi}
If they presented this to me in school, I wouldn’t have failed.
Thank you Sir!
My pleasure, thanks for watching!
if the question is about the caldinality, how can I answer if it is a letter
Sir can I answer these quickly what r the cardinals numbers of the set of 10 3 4 6 11 16 19 20
Thanks for watching, Andrew! To find the cardinality of { 10, 3, 4, 6, 11, 16, 19, 20 }, we just have to count the distinct elements! Let me know what you get, and if you want to see some examples, check out this lesson: th-cam.com/video/KmHMot3OIQs/w-d-xo.html
Let me know if you have any more questions!
What is the cardinality of set {0,{0},{0,{0}}} ? can plz explain
thank you for your video!
You're very welcome, thanks for watching!
Bro I have a question. I am studying for my CCNA exam and in binary for 2 to the power of 0 equals 1. I have no idea how that is possible, any ideas as to how this is possible
THANKS
No problem, thanks for watching!
this is rly helpful thx
Glad to hear it! You're welcome and thanks for watching!
Can you tell me how can I find or if is possible to find e cardinality for a set that goes like this {1,2,3,......n}
I am sure I've done this before but forget it by now
Thanks for watching! I am not sure I understand your question. The set {1, 2, 3, ..., n} must have precisely n elements - the integers 1 through n. Does that answer your question or am I missing something? Is it perhaps the notation in which the set is written that makes you unsure?
Cardinality of A={1,25,11,z,b,c?
THANK YOU FOR THIS
I SUBSCRIBED
So glad it helped! Thanks for watching and subscribing!
you are the best thank you soo much
You're welcome and thanks so much for watching! Let me know if you ever have any video requests!
good vid keep the good work
Thank you.
M={5,10,15,20}
How do I illustrate M?
pls.reply
so in B the set {1,2} has a cardinality of 1 or 2 elements ? beacuse if it has a cardinality of 2 then (the empty set ) has a cardinality of 0 and 3 has a cardinality of 1 so in total we have a cardinality of 3, or do we count {1,2} as a 1 and 3 as a 1 and the empty set as 1 , also what about the cases where the set is an element of itself like ( the power sets) do we count the empty set and the set itself sorry if it sounds confusing but im a bit confused
Thanks for watching and for the question! But it was hard to follow because you are talking about the cardinality of 3, and 3 is a number - not a set - so I am not sure what you mean when you refer to its cardinality. The set {1,2} certainly has cardinality 2 because it has 2 elements, namely 1 and 2. Also, at least in the majority of treatments of set theory, a set being an element of itself is not possible. The power set of {1,2}, denoted P({1,2}), for example, includes {1,2}, which might be what you mean. But the power set of {1,2} does not contain itself, that is: P({1,2}) does not contain P({1,2}).
Hmmm how about ...... How to find the elements in intersection of A,B??
bro can u help this question quckly {θ,{a,b}}?
What is cardinality of {1, 1,2,3,2,4} just example... If set contains double numbers
Thanks for watching and good question! Sets do not allow for repeated elements, or put another way, they do not distinguish between an element occurring once or repeatedly. So, {1, 1, 2, 3, 4, 3, 4} is the same set as {1, 2, 3, 4} and that should answer your question about the cardinality!
Can you explain to me the statement "
A subset of a power set.
info
About
(a)
Let X = {a, b, c, d}. What is { A: A ∈ P(X) and |A| = 2 }?
"
I basically don't understand the builder notation means? And does that mean A only has two elements in them?
Thanks for watching and for your question! I’m a little confused by your comment, but let me answer the question you ask at the end and hopefully that helps. Remember that if X is a set, then the power set of X, P(X), contains all subsets of X. So each element of P(X) is a subset of X. The set builder notation you provided means take all elements A of P(X), such that |A| = 2. So take all elements of P(X) that have only two elements in them. In other words, take all 2 element subsets of X, that’s what that set builder notation describes.
So let’s say your set builder notation set is called B. Here is a subset of X ( which is an element of P(X) ): { a, b, c }. This element of P(X) will not be in B because it contains 3 elements, not 2. Here is another element of P(X): { a, b }. This will be in B because it is an element of P(X) and it has exactly 2 elements.
So again, the set builder notation you provided, that describes a set we call B, contains all 2-element subsets of X. The key to making it easier to understand is recognizing “an element of the power set of X” as “a subset of X”. Does that help?
❤❤thanks🙏
Glad to help!
sir mean lAl< this kind of line represent cardinality
Thanks for watching and for the question! That's right! If A = { 1, 2, 3 } for example, then the cardinality of A is 3. So, |A| = 3 because |A| denotes the cardinality of A. Remember that the vertical bars are used in many contexts to denote a sort of "magnitude". For example, if AB is a line segment from point A to point B, then |AB| usually denotes the length of the segment AB. If x is a real number, |x| denotes the absolute value of x, those are just a couple of examples. In the case of set theory, |S| denotes the "magnitude" of S, which in this case is measured as cardinality. Does that help?
nice one
Thanks for the lesson but I wanna learn what symbol to use to indicate the intersection of the two sets
Thanks for watching and here is my lesson on set intersection: th-cam.com/video/mOMoZYGirQQ/w-d-xo.html
thx this help alot
Glad to hear it, thanks for watching!
Helped me thanks
Glad it helped, thanks for watching!
thx a lot :D
No problem - thank you for watching!
Ik am super late but I have a q if the set have a duplicate element should we count it as well?
Nope, sets have distinct elements. So the set { a, b, c } is the same as the set { a, a, b, b, b, c, c, c, c }.
There are contexts when multisets are considered, that is - sets where each element could occur a number of times, but if you're just learning about sets then no, duplicate elements are not counted.
@@WrathofMath I meant in the context of cardinality.
And thx for reply btw man ur great.
Sir, thank you so much. So basically you're just counting how many elemenrmts are there in a subset?
You're very welcome! And I'm not sure what you mean by including "subset" in your question. Yes, to find the cardinality of a set we just count the number of elements in the set. Of course, some sets have infinitely many elements, either countably infinite [like the naturals] or uncountably infinite [like the reals]. Subsets are also sets, so this applies to them as well. Does that clear it up?
@@WrathofMath Yes, thanks again!
({a,b}) cordinality plxx????
When youtube is better than the teacher
👇🏿
Thanks for watching and I am glad it helped!
It's actually it's because of the tension the teachers give off, the reason why the you are affected by the teacher's tension is because they are capable of touching you, they can even do something to you, or do something on your social life, in short you feel fear, so you can't really focus on the teachings, and this guy is not capable of doing anything to us, not capable of ruining our social life, that's why we understand him better than the teachers
Given:F = factors of 4
1.Write F in roster method
2.write f in set builder notation
3.what is the elements of f?
4.what is the cardinality of f?
5.give 3 at least equal to f
6.give atleast 3 sets equivalent to f
7.list all the subsets of f
8.list all the proper subsets of f
-pls someone help can someone give me clue how to solve this i dont know how
Your teacher didn't tell you how?
Now I get it!
Awesome! Thanks for watching!
i have trouble doing it :(
What is the cardinality of the concatenation of two sets?
cardinality of set is the size of the set?
Is n in n(m) symbolized cardonality?
When talking about sets, yes, that's pretty common notation for cardinality. Thanks for watching!
@@WrathofMath thank you
i have a doubt
cardinality of set p(p(p()))?
How about the cardinality of set A = {0}? is it 1 or 0?
Thanks for watching and let me turn the question back to you! Does our set A = { 0 } contain anything?
@@WrathofMath 1 ?
hello sir can yu plz solve this
Consider the following ORACLE relations:
One (x, y) = {, , , , , }
Two (x, y) = {, , , , , , , }
Consider the following two SQL queries SQ1 and SQ2:
SQ1 : SELECT * FROM One)
EXCEPT
(SELECT * FROM Two);
SQ2 : SELECT * FROM One)
EXCEPT ALL
(SELECT * FROM Two);
For each of the SQL queries, what is the cardinality (number of rows) of the result obtained when applied to the instances above?a.2 and 1 respectivelyb.1 and 2 respectivelyc.2 and 2 respectivelyd.1 and 1 respectively