How to Identify the Elements of a Set | Set Theory
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- Опубліковано 29 чер 2024
- Sets contain elements, and sometimes those elements are sets, intervals, ordered pairs or sequences, or a slew of other objects! When a set is written in roster form, its elements are separated by commas, but some elements may have commas of their own, making it a little difficult at times to pick out the elements of a set.
In this lesson, we go over the process of identifying the elements in some nasty sets, and provide an example problem at the end.
Additionally, if you can identify the elements of a set, you can count them! And if you know how many elements are in the set, then you can figure out how many subsets it has, which is also the cardinality of its power set! Hope you enjoy the lesson!
I hope you find this video helpful, and be sure to ask any questions down in the comments!
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The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow's music, and wanted to share it with those of you watching. Please check out all of his wonderful work.
Vallow Bandcamp: vallow.bandcamp.com/
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Vallow SoundCloud: / benwatts-3
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When I was in elementary my teacher, our classmates, and me always wathching your math videos, very nice videos about mathematics😊
Thanks so much, Althea! I am so glad the lessons have been helpful for you!
I'm from Romania and I know English and for school when I don't understand what my teacher said I'm coming on your channel and watching your videos to understand much better,thnx for help you are doing a great work
So glad to help, thanks for watching!
literally saved me... Thank you from the bottom of my heart.
Glad to help!
online class is so boring so i had to watch a vid thanks btw
So glad it helped, thanks for watching! If you're in the mood for some math that isn't boring, I strongly recommend my newest video about the infamous S drawn by middle schoolers the world over! ua-cam.com/video/uEJQubc0PPU/v-deo.html
how is N (nartual number) C W (whole number) is it because of it both not having brackets?
Thanks your knowledge share for use thank you cause now I already understand!
You're welcome, I am so glad it helped! Thanks for watching!
1. M = {x | x > 6, x is an odd integer}
2. A = {x | 9 < x < 10, x is a counting number
3. T = {x | x is a city in Metro Manila}
4. H = {x | x is a counting number between 4 and 28}
5. S = {x | x is a set of days with names containing x}
help me
😵😵😵😵😵
😵💫
Is this a joke or something? But M = 7, 9, 11, 13, etc. if I'm not wrong.
Grade 7?
Thanks for your help
No problem, thanks for watching!
this channel really helps me in my shcool works💖
Glad the lessons help! Thanks for watching and let me know if you ever have any questions!
@@WrathofMath i need to answer my module..heheh..... can you help me....what are the set of this ..bus,motorcycle,jeep,taxi
I have a question
In terms of phi/empty set we should count as a element or not??
How we distinguish sir the elements of X'
( 2, 3, 2) is element of S
{ 1, 3, { } } is element of S
[ 1, 4, ] is element of S
{ ( 2, 5 ), 8, 6, { 1, 9, } , 4 } } is element of S
Greetings, can you please let me know if I did this correctly? Ty and have a great day
Yes,you are
Yes you are correct, but you delete this curly bracket at the end (because you have 2 curly brackets in a row at the end). and it will be fine
So in 2^2 x 3^2 what would the elements be?
धन्यवाद महोदय
So If we r writing a subset we want to put curly brackets and if we r writing a element no need of bracket?
Thankyou🥰
Please sir help me out. How do I answer this maths / A set has 4 elements find the number of subset
For the first example is 3 an subst of of yes or no ?
Sir help with this one, how many subsets has set A given that set A=(a, c,1,0,4,2,10,12)
Given, no of elements (n) = 8
So, P(A) = 2 raise to n
= 2 raise to 8
= 256
B={phi,3,{5,{9,10},12,13,4{15},18,20}}} how many element sir please answer . I need very much
The best example ulike the others .they provide examples for preschooll
Haha, I'm glad you found my examples helpful! Thanks for watching!
Lol i got annoyed and raged at my math assigmment but thanks to u i understand
I'm glad the lesson helped! Hopefully it brought you back to a state of tranquility. Thanks for watching and let me know if you ever have any questions!
i am 8 and this is my lesson
exactly 5 elements,roster method
Thank you sir
You're welcome! Thanks for watching!
Can you tell me how we find product means (A*B)
of these type of set A= { {6,4}, 2, 8} ,
B= { x , { p, w, z} ,4 , k }
My request please tell me as early as possible
What the answer of n(A)
Do you mean, how many elements does A have? That depends on what A is! If n(A) is the cardinality of A, it is simply the number of elements in A if it has a finite number. Otherwise, it is infinity.
Your so smart man
I just do a lot of math; study, and you will learn just as much! Thanks for watching and let me know if you ever have any questions!
How to take Union of such sets?
In one of your video you have said that , the cardinality of power set can be expressed by this equation 2^n , where 2 is showing the possibility of element either being a part of subset or not. But when we actually define a power set , can you please explain how this equation actually work? I mean assume we have a set with two elements,and for the power set two elements will always be an empty set and a set itself , so how does the formula works?
I'm not totally sure what your question is, but this video might answer it: ua-cam.com/video/7C7I8SSsXaE/v-deo.html
And if it helps explain things at all, I'll quickly touch on the two sets you mentioned. For any set S, the empty set and the set S are subsets of S. Like you said, the 2^n formula comes from the fact that for each element in a set, we have two choices when making a subset. Include it or do not include it. The empty set is the subset we get when we choose to not include any. The set S is the subset we get when we choose to include every element. I hope that and the video I linked to helps clear up your question but if not - try explaining your question to me some more and maybe I can help!
@@WrathofMath exactly answered my question . Thanks mate , you just made my day, I came up with the same logic but I just wanted to confirm that was it the right logic or not!
Nice work! Yeah that's what I think is the simplest reasoning that leads to the 2^n conclusion. But of course there are many ways to get to the same conclusion most of the time, which can be great for checking our answers and for explaining things when someone doesn't understand a certain way.
For example, if we have a set with 3 elements, how many subsets does it have? Easy, 2^3 = 8. But what if we wanted to try using a different solution method? We are trying to count subsets, so this is a counting problem (the type of problem that we often solve with permutation or combination calculations). We also know that order doesn't matter since these are sets. So knowing that this is a non-ordered counting problem, we might be inclined to try using combinations. Indeed, to count the number of subsets a set with 3 elements has, we could count the number of combinations of 0 elements possible, the number of combinations of 1 element possible, the number of combinations of 2 elements, and of 3 elements, and add them together. This is because a subset is just a combination of the elements in the original set.
This would give us C(3, 0) [this is read 3 choose 0, it's the number of ways 0 objects can be chosen from a collection of 3] + C(3, 1) + C(3, 2) + C(3, 3) = 1 + 3 + 3 + 1 = 8. Much less efficient, but another valid solution!
Can I write 3,4 E S ??
THANK YOU SOOO MUCH NOW I I UNDERSTAND 😁😁😀
Glad to hear it! Thanks a lot for watching!
Hello, my question is can the numbers
{ 1.5 , 2.5 , 3.5 }
Be a element ?
Thanks for watching and I'm not completely sure what your question is. Sets can contain anything, so 1.5, 2.5, and 3.5 can all be elements of a set. Even the set containing them: { 1.5, 2.5, 3.5 } can be an element of a set! Does that help?
@@WrathofMath yess , thank you !
Thanks po 😁😁😁 it really help
Glad to hear it!
In the 1st curly bracket, we counted as 1 element before there is a close bracket, but didn’t do the same in the 2nd curly bracket. What’s the meaning of that Sir? I’m lost
That's because the first curly bracket has "opened up an element" and thus there will not be a second element until that first curly bracket is closed. When another open bracket appears, we now have two brackets that need to be closed before we can move on to a new element. Does that make sense?
You are genius
Thanks for watching, and hopefully you're a genius of identifying set elements now!
How do I define and write the elements of these sets?
A= {x: -1< x
This is probably late but here it is:
A = { 0, 1, 2, 3, 4} (for those who are confused, x E Z means x is an integer. The E should actually an "element of" symbol as shown in the video.)
B = { 0, 1, 2, } (Not sure about this but W means whole numbers so it must not have negative numbers.)
C = { 11, 12, 13,..., infinity symbol) (Replace the infinity symbol with the actual infinity symbol since I don't know how to type it on keyboard. N means natural numbers).
This is probably late but here it is:
A = { 0, 1, 2, 3, 4} (for those who are confused, x E Z means x is an integer. The E should actually an "element of" symbol as shown in the video.)
B = { 0, 1, 2, } (Not sure about this but W means whole numbers so it must not have negative numbers.)
C = { 11, 12, 13,...) (Do not forget the "..." since it means the list goes on forever. N means natural numbers).
Thanks for the valued shared but u have a question.
Is this illustration true or false?
Is 1 an element of {2,(1)}
Thanks for watching and that depends on what (1) is. If it is the 1-tuple with the first element of 1, then 1 is not an element of {2, (1)}. If (1) is just like (0+1), as in the parentheses are those we see in arithmetic, then (1) = 1 and so 1 would be an element of {2, (1)}.
@@WrathofMath So it's guaranteed to be false if it had been {1} instead of (1)?
S = {factors of 6}
whats the element
which software is used for this video
Really thanks I got it
You’re welcome, I’m glad it helped! Thanks for watching!
How can you explain this?
A={a} is not equal to B={{a}}?
I don’t know how I understand it but I do
Thanks for watching! You understand because you put in the work to study and comprehend the concepts! Good work and let me know if you ever have any set theory questions!
Achukas :D ok
really helpful and sorry sir i was busy because of this i didnot view your video
Thanks for watching, and that is perfectly fine! I'm happy for you to watch whichever videos you have time for and are most helpful for you!
Answer of your question is - 4 elements.
Right on, good work! I'd recommend not separating your answer from other text using math symbols like hyphens if you can avoid it! In this case of course it is pretty obvious you don't mean negative four due to the context. Thanks for watching!
То чувство, когда тебя заставляют учить это
How elements important to a set?
Thanks for watching, Gene! I'm not sure I understand your question. Sets, generally speaking, contain objects, and those objects are called elements. It is the fact that sets can contain elements that makes them so extraordinarily useful in our formulation of mathematics. However, sets don't HAVE to have elements, since there is an empty set.
The answer would be 4
😊
1️⃣4️⃣8️⃣8️⃣
Thanks for watching, Alex! Do you have a question I can help clear up?
whyyyyy is math sooooo hardddddddddddddd whats the elements of a b help me pls
my brain hurts
That's no good! Let me know if you have any questions, go get a scalp massage to soothe the brain or something!
Can i use words instead of numbers?
Thanks for watching and I am not sure what you mean, some sets may contain words, some sets contain numbers, sets can contain anything! Does that answer your question?
How many elements in the set {c,{c},{{c}}}
Thanks for watching, how many do you think?
@@WrathofMath 3
GGG bro
Wtf
Do you have a question I can help answer?
Thanks sir
Glad to help! Thanks for watching!