Mark this explanation is beyond brilliancy, I’ve managed to grasp all this set notation properties because of your brilliancy at explaining mathematical concepts, suscribed and life is good fam
for supremum definition, #3 shouldn't it say the largest instead of the smallest number greater than or equal to all the numbers in the set ? and also for infimum definition, #3 should it be the smallest number less than or equal to all the numbers in the set instead of saying " the largest number " ?
Hi Rebecca! It seems backwards at first glance but it is actually the right way in the video! Consider all real numbers between 3 and 4 (not including 3 and 4). Then 5 is larger than all of these numbers. So is 4.8, 4.1, 4.01, and 4. The supremum is the smallest of these numbers 4. We want an upper bound on the numbers, but we want the tightest upper bound that we can get.
John Smith When the set is empty, then every number is an upper bound on the set. So -1 is an upper bound, -100 also an upper bound, -1000000 and so on. So the smallest number that is still an upper bound is effectively negative infinity!
Mark Huber I guess what I don't get is the supremum of the set {1,2,5} is 5. but when it's empty its any negative number? Why wouldn't it be any positive number since positive numbers are larger.
it's not exactly about "any negative" it' about "SMALLEST upper bound". it means you take the smallest number that is larger than all the other, so -inf is very small, but it's still larger then all other cuz set is actually empty
John Smith shota jolbordi Shota is exactly right here: the supremum isn't just any upper bound, its the smallest upper bound. In your first example of {1,2,5}, 6 is an upper bound on all three of those numbers, so is 5.5. But 5 is the *smallest* upper bound on those three numbers, so that is the supremum. If your set {} is empty, then 2 is an upper bound, but so is -2--just because -2 is larger than all numbers in the set! So is -3, -4, and so on, so the smallest number that's an upper bound on all the (nonexistent) numbers in the empty set is considered to be negative infinity.
One way to think about it: when a number is added to a set, the supremum can either stay the same or go up, because it is an upper bound on the set. So when we move from the empty set to a set with some element, the supremum can only stay the same or go up. And the only number that "goes up" to any other number is negative infinity!
I think you missed the most important cases when the supremum/infimum are not -infty, infty or the maximum/minimum from a set. For example, if you have the set S = {3, 4, 5, 6, 7, 8} and a subset T = {5, 6}, the supremum of T is 7 and the infimum is 4, as they are the smallest upper bound and greatest lower bound of T inside S, respectively.
Usually we apply infimum and supremum with respect to the reference set of the real numbers. But even in your example, the supremum of T is actually still 6 since 6 is also inside S.
Remember, with the infimum we are looking for a number *smaller* than all the numbers in the set. The only number smaller than all the numbers {0, -1, -2, ...} is -infinity!
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really simple explanation with minimal jargon to throw off someone nervous or unsure about the concepts. Thanks a lot!
Mark this explanation is beyond brilliancy, I’ve managed to grasp all this set notation properties because of your brilliancy at explaining mathematical concepts, suscribed and life is good fam
this explanation was supremely brilliant with minimum (rather infimum) data. Simply, it was concisely bounded!
Very simple explanation and straight to the point. Kudos👍🙏
Absolutely amazing and concise explanation!
Such a wonderful piece of work this is. Helped me with my exams.
Glad it helped, that's great!
so much knowledge in 3 min. thank you
for supremum definition, #3
shouldn't it say the largest instead of the smallest number greater than or equal to all the numbers in the set ?
and also for infimum definition, #3
should it be the smallest number less than or equal to all the numbers in the set instead of saying " the largest number "
?
Hi Rebecca! It seems backwards at first glance but it is actually the right way in the video! Consider all real numbers between 3 and 4 (not including 3 and 4). Then 5 is larger than all of these numbers. So is 4.8, 4.1, 4.01, and 4. The supremum is the smallest of these numbers 4. We want an upper bound on the numbers, but we want the tightest upper bound that we can get.
@@MarkHuberDataScience thank you so much for your reply and explanation
I appreciate it
Well done! Concise and informative!
Excellent Presentation. Thank you sir. Thank you so much. specialy for example.......
why is it negative infinity if the set is empty. for supremum
John Smith When the set is empty, then every number is an upper bound on the set. So -1 is an upper bound, -100 also an upper bound, -1000000 and so on. So the smallest number that is still an upper bound is effectively negative infinity!
John Smith so when the set is empty any number is "the largest" so even the smallest possible number (hence - infinity) is "the largest"
Mark Huber I guess what I don't get is the supremum of the set {1,2,5} is 5. but when it's empty its any negative number? Why wouldn't it be any positive number since positive numbers are larger.
it's not exactly about "any negative" it' about "SMALLEST upper bound". it means you take the smallest number that is larger than all the other, so -inf is very small, but it's still larger then all other cuz set is actually empty
John Smith shota jolbordi Shota is exactly right here: the supremum isn't just any upper bound, its the smallest upper bound. In your first example of {1,2,5}, 6 is an upper bound on all three of those numbers, so is 5.5. But 5 is the *smallest* upper bound on those three numbers, so that is the supremum. If your set {} is empty, then 2 is an upper bound, but so is -2--just because -2 is larger than all numbers in the set! So is -3, -4, and so on, so the smallest number that's an upper bound on all the (nonexistent) numbers in the empty set is considered to be negative infinity.
Thanks Mark!
SIR WHEN THE SUPREMUM IS INFINITY , THAN WHAT WILL BE THE UPPER BOUND ???
infinity
Simple and clear it was of help thanks
Very helpful. Thanks much!
thank you¡ very clearly explained
Some logical questions
1) When the set of numbers is empty, why the supremum is negative infinite? why not positive infinite? Please clarify.
One way to think about it: when a number is added to a set, the supremum can either stay the same or go up, because it is an upper bound on the set. So when we move from the empty set to a set with some element, the supremum can only stay the same or go up. And the only number that "goes up" to any other number is negative infinity!
may God gives you more kudos
Amazing!
very nice video and a very nice elaboration... :)
thanks, this is so clear.
Lol can my math teacher please take a course on presentation from you? Half the lectures I don't even know why I came to class
Thank you Mark!
thankful for your videos
which app you have used for making this vedio
It was made using PowToon. Highly recommended!
I think you missed the most important cases when the supremum/infimum are not -infty, infty or the maximum/minimum from a set. For example, if you have the set S = {3, 4, 5, 6, 7, 8} and a subset T = {5, 6}, the supremum of T is 7 and the infimum is 4, as they are the smallest upper bound and greatest lower bound of T inside S, respectively.
Usually we apply infimum and supremum with respect to the reference set of the real numbers. But even in your example, the supremum of T is actually still 6 since 6 is also inside S.
Thank you so much
Super mathed for explaintion
Sir @markhuber plz upload a video on Archimedean property same as this video...plzzz sir
superb
Great!
Thank you
Very nice, thank you...
nicely explained
thank you so so much
Clearly! Thanks.
Thanks, it helped a lot
Haoyu Li you are asian you are supposed to know these things
TNX A BUNCH :)
MOAR :D
So helpful
Thank you so much! The video is cute and well-explained.
Wonderful. Thanks
Nice
wish I saw this when I took a class talking about this
Sir u r awesome...
so nice and helpful. many thanks!!
thank you
You're welcome!
Excellent explanation! Thx, yo
omg thank you so much for this video. it made it so simple.
Thanks!
Super
Inf{ 0,-1,-2,-3......} =-infinity ? How ?
It must be 0(zero)
Remember, with the infimum we are looking for a number *smaller* than all the numbers in the set. The only number smaller than all the numbers {0, -1, -2, ...} is -infinity!
@@MarkHuberDataScience yes get it
حلووو
thx
blz
we are sorry to inform you that trough your use of musical choices you will have to go to jail for a supremum of 3 years, have fun
Thank you so much
Thanks a lot
thank you very much
Thank you very much