At 6:30, you proved that x is an element of B, which proved that A is subset of B. How do we prove that A is a proper subset of B? The set A has fewer items than B, but i dont know how to write it in a math way. Last question, the method of proof you used in this video is direct proof, right? Thanks.
nice video , but i could not grasp the idea of putting q=2p yeah it's logical, but you made a specilization here by making q=2p, what if they p and q equal each other or p is 3q or anything else .. thank you
@@DrTrefor So p and q are different integers to define different sets so that the first set A have all numbers which are multiple of 4 and the second set B have all numbers which are multiple of 2 .. you need to proof that Set A is a subset B so you need to verify that each element in A is also in B. There is just one case that makes the numbers in A is subset of B, that's when q=2p .. that means that you must choose an even number for q to make sure that it is in the two sets. If you choose odd number it will be in B but not in A. Hence the set A is subset of B. You could say also because every number in A is a multiple of 4 that leads to every number of A is also a multiple of 2. This example is easy but if there is two other complex sets and you want to see if one of them is a subset of the other ? Thanks
because the definition of q is that its an integer, and p was also defined as an integer, 2p would also be an integer because integers are closed under multiplication.
i dont understand the letters you use for this and the next few videos, you use n and m to describe the elements of A and B but you use n for both such that statements. is there a reason for that ? at first i thought you used n for both because A is a subset of B but then i saw you did that for the union and intersection in the next few videos as well.
@@iAnarchy89 the top says n is a in the integers Z and that n will be 4 times some integer p (also an integer). The bottom says m is an integer such that m will be 2 times q (also an integer). I am studying maths too but I'm pretty sure there should be an m in the bottom set builder (where in the video is an n). I've emailed the professor and am awaiting a response.
@@nateburd ahhh sorry I misunderstood your earlier reply, I thought you meant my comment was wrong haha. Thanks it was bugging me thought my understanding of the concepts were wrong.
At 6:30, you proved that x is an element of B, which proved that A is subset of B. How do we prove that A is a proper subset of B? The set A has fewer items than B, but i dont know how to write it in a math way. Last question, the method of proof you used in this video is direct proof, right? Thanks.
Yes, it is a direct proof. If you want to say A has fewer items than B, you can say |A|
Looks like there is a small typo in example from 2:54 Set Builder notation for B should use m in the condition part, not n
very helpful. thank you
Wow it took 6 minutes and I understand this and it took my professor 1 hour and confused a whole bunch of people
nice video , but i could not grasp the idea of putting q=2p
yeah it's logical, but you made a specilization here by making q=2p, what if they p and q equal each other or p is 3q or anything else .. thank you
@@DrTrefor So p and q are different integers to define different sets so that the first set A have all numbers which are multiple of 4 and the second set B have all numbers which are multiple of 2 .. you need to proof that Set A is a subset B so you need to verify that each element in A is also in B.
There is just one case that makes the numbers in A is subset of B, that's when q=2p .. that means that you must choose an even number for q to make sure that it is in the two sets. If you choose odd number it will be in B but not in A. Hence the set A is subset of B.
You could say also because every number in A is a multiple of 4 that leads to every number of A is also a multiple of 2.
This example is easy but if there is two other complex sets and you want to see if one of them is a subset of the other ?
Thanks
I love you Trefor. Thank you.
great video i would just say in future please write more clearly - thank you for your effort, much appreciated.
Thanks sir
Nice video, very helpful, do note that you started with nice hand writing but you started accidentally used italic font towards the end.
Why can you let q = 2p?
because the definition of q is that its an integer, and p was also defined as an integer, 2p would also be an integer because integers are closed under multiplication.
i dont understand the letters you use for this and the next few videos, you use n and m to describe the elements of A and B but you use n for both such that statements. is there a reason for that ?
at first i thought you used n for both because A is a subset of B but then i saw you did that for the union and intersection in the next few videos as well.
@@DrTrefor so can i say
A = { n ∈ Z | n = 4p, p ∈ Z}
B = { m ∈ Z | m = 2q, q ∈ Z} ?
@@iAnarchy89 I think it is incorrect. The set variable should be indicated in the set build.
@@nateburd hi I don’t understand, what is the m there for?
@@iAnarchy89 the top says n is a in the integers Z and that n will be 4 times some integer p (also an integer).
The bottom says m is an integer such that m will be 2 times q (also an integer).
I am studying maths too but I'm pretty sure there should be an m in the bottom set builder (where in the video is an n). I've emailed the professor and am awaiting a response.
@@nateburd ahhh sorry I misunderstood your earlier reply, I thought you meant my comment was wrong haha. Thanks it was bugging me thought my understanding of the concepts were wrong.
2p+1 is odd if p is whole. If p is .5, it’s even.
do you know what an integer is
decimals are not integers
You're the Mensan version of Mac from IASIP
I think P also belongs to positive integer rather than integer only sir , in order to make n a positive integer . or may be I'm wrong😁