I didn't know (or didn't remember) that definition for the supremum/infimum of the empty set, interesting!
@jgsh80622 жыл бұрын
These videos are awesome, thanks so much! I got a book on real analysis, but it was waaaayyy too terse to be used as a learning tool on its own. These are really helpful!
@brightsideofmaths2 жыл бұрын
Thank you :)
@PunmasterSTP2 жыл бұрын
Supremum? More like "This is free, man!" Thanks for making and sharing these amazing videos.
@darthtleilaxu40212 жыл бұрын
Bonjour !😎 It's me again. Another little difference! In France, we write ]a,b] instead of (a,b].
@brightsideofmaths2 жыл бұрын
Yes, this is common notation and I also like it.
@ansumanc Жыл бұрын
another reason to hate france
@alikemaliltusАй бұрын
Unhinged notation😮 but it makes sense
@allenfdo8813 Жыл бұрын
Thank you so much for making these videos!
@brightsideofmaths Жыл бұрын
Glad you like them!
@DOROnoDORO2 жыл бұрын
It always blows my mind that open intervals don't have maximal / minimum elements. weird stuff
@rajinfootonchuriquen Жыл бұрын
Given the definition, it's very natural. If you search for hyperreal numbers, then the maximal and minimum of an open subset of the hyperreal numbers is just the supremum of the real - infinitesimal for the maximum and infimum of the real + infinitesimal for the minimum, if you like to think in that way, the supremum is the standard part of the maximum of an "open" interval.
@faith_jelagat_ Жыл бұрын
Thank you so much. Great explanation!!!
@brightsideofmaths Жыл бұрын
Thank you very much :)
@prakashchandracharan9565 Жыл бұрын
But then it means phi is such a set for whom sup
@brightsideofmaths Жыл бұрын
Yes, for the empty set, this inequality is not fulfilled :)
@somerikcharan8555 Жыл бұрын
Thank you very much sir.
@blablablerg Жыл бұрын
Very nice and clear explanation!
@brightsideofmaths Жыл бұрын
Glad you liked it
@sumittete28042 жыл бұрын
Sir ...what are the supremum and infimum of (0,1) intersection {m+n√2 : m,n are integers}?
@moowmotors2 жыл бұрын
thanks a lot!
@dhirajghadage43423 жыл бұрын
In the definition of supremum, you said that all "x" in "M" are such that "x" is less than or equal to "s" that means "x" can be equal to "s" and "s" may be the part of "M" but "s" isn't part of "M" . I thought definition of supremum should be all "x" in "M" are such that "x" should be less than "s".
@brightsideofmaths3 жыл бұрын
s could be an element of M.
@dhirajghadage43423 жыл бұрын
@@brightsideofmaths if s is the element of M then it should be called as maximum and not the supremum.
@brightsideofmaths3 жыл бұрын
@@dhirajghadage4342 The supremum could also be a maximum. This doesn't invalidate the properties of the supremum.
@dhirajghadage43423 жыл бұрын
@@brightsideofmaths In which case supremum could be maximum?Can you give any example set. For example- In set [1,3] 3 is the maximum and in set (1,3) 3 is the supremum like these.
@brightsideofmaths3 жыл бұрын
@@dhirajghadage4342 For the set [1,3], the point 3 is the supremum (and also the maximum).
@qiaohuizhou69603 жыл бұрын
5:53 two properties of sup 7:20 sup of empty set
@brightsideofmaths3 жыл бұрын
Can I use your bookmarks as the official video bookmarks? :)
@qiaohuizhou69603 жыл бұрын
@@brightsideofmaths Yes!sure! I am glad to help!
@brightsideofmaths3 жыл бұрын
@@qiaohuizhou6960 Of course, I am always if one helps with bookmarks, subtitles and so on. I am not always able to do everything myself :)
@TallSky6669 ай бұрын
love supwemum and weal numbers! so gweat
@brightsideofmaths9 ай бұрын
:D Don't make fun of people with speech disorder!
@physicswithmarya Жыл бұрын
Thank you!
@user-yc5mw1ww2x10 ай бұрын
Thank you so much that was extremely helpful !
@VaheTildian Жыл бұрын
For the definition of supremum of M, is it important to say that the real S is greater or equal to any X of M ? Instead, could it be "S is strictly greater than any X of M" ? Or it is a kind of convention, so a supremum can also be a maximum if the the real S is part of M ? Also, for the 2nd point definiting the supremum of M, could we say instead "For any E greater than 0, S - E belongs to M" ? I feel like it could work the same way, without using x tild as an intermediate. What do you think?
@VaheTildian Жыл бұрын
I'm back here to answer my own 2nd question It is better to use an x~ because then we dont have to care that the precise number S-E is inside M. Maybe M is not a continous line but a collection of points. Then it is possible that S-E is not in the set M. But S-E would still be interesting if you compare it to another point of M that is greater than it. That's why x~ is interesting, as it allows E to be any value greater than zero, and still be used to define the supremum
@lourdesmartinaguilar5124 Жыл бұрын
Thank you it was very useful 😊
@thecutepro24474 ай бұрын
you are my sunshine❤TY for your videos good❤
@triton626742 жыл бұрын
How can the inf of a set be greater than the set's sup?
@brightsideofmaths2 жыл бұрын
No this can't happen. Why do you think that?
@MrScattterbrain2 жыл бұрын
@@brightsideofmaths , since sup of an empty set is minus infinity, and inf of an empty set is plus infinity, then (at least heuristically) we can say that for the empty set inf is greater than sup. This would be avoided if inf and sup of the empty set were left undefined, I guess.
@brightsideofmaths2 жыл бұрын
@@MrScattterbrain Yeah, you are right. The empty set is an exception here. Nevertheless, the definition is very helpful in a lot of contexts.
@mueezadam84383 жыл бұрын
In the final example, is s - epsilon not an upper bound because it’s the maximal element?
@brightsideofmaths3 жыл бұрын
Be careful: A maximal element is always an upper bound by definition.
@Katokoda3 жыл бұрын
I would use ]1, 2] to denote your (1, 2]. That means using [,] as a closed subset, ], [ as an open subset, and choosing that for each borders It is most of the time similar, but it is easier when you want to distinct (1, 2) and ]1, 2[
@brightsideofmaths3 жыл бұрын
Of course, use another notation if it fits your style and helps you! However, my notation here is also very common and therefore one needs to understand it as well.
@joshuaokoro27813 жыл бұрын
Why is the infimum of an empty set is equal to positive infinity? And supremum of an empty set is equal to negative infinity? Is there anything hidden here?
@brightsideofmaths3 жыл бұрын
Good question. Of course, it is just a definition. However, it is a useful one because it guarantees that the supremum does not get smaller when you add points to a set.
@parthvarasani4958 күн бұрын
@@brightsideofmathswhat if we add a point greater than supM in set then ?
@brightsideofmaths8 күн бұрын
@@parthvarasani495 The supremum gets bigger than :)
@kaos0922 жыл бұрын
If a number is excluded from a set such as (2,5] then how can 2 be the infimum of a set?
@brightsideofmaths2 жыл бұрын
By definition of the infinum: inf and sup are always well-defined real numbers. That's the difference to the minimum and maximum :)
@gileadedetogni9054Ай бұрын
The infimum doesn't need to be in the set
@shourjyobiswas2999 Жыл бұрын
beautifully presented
@brightsideofmaths Жыл бұрын
Thank you! Cheers!
@lalhriatpuiahmar50572 жыл бұрын
Sir what is x (tilde)??
@brightsideofmaths2 жыл бұрын
Just a name for a number :)
@islamatef25266 ай бұрын
Do you have an explanation on your channel about the topic of quantum numbers q-binolmial? q-derivative etc ?
@brightsideofmaths6 ай бұрын
Not yet, sorry!
@joaopedrodiniz7067 Жыл бұрын
The way i learned in my book (which is quite old) is the following definition: x is called a supremum of a set M if it it is true that: 1) x is an upper bound; 2) for all upper bounds y, x is smaller or equal to y. The infimum is similarly defined, and upper/lower bounds has the same definitions as in your video. Is this definition of supremum and infimum still used today, or is it "outdated"? And also, great video! Thanks so much!
@brightsideofmaths Жыл бұрын
Yes, it's the same thing :)
@glennlehman9608 Жыл бұрын
Is supremum the same thing as least upper bound?
@brightsideofmaths Жыл бұрын
Yes!
@vishakhadasi36262 жыл бұрын
thankyou!!
@brightsideofmaths2 жыл бұрын
You're welcome!
@dariacatrinoiu16772 жыл бұрын
danke:]]
@tipsandyouu13372 ай бұрын
Sir did u learn all these things from Book 100% teaching level❤
@brightsideofmaths2 ай бұрын
Thanks! I studied mathematics for many years :)
@tipsandyouu1337Ай бұрын
@@brightsideofmaths that's why so
@user-dq7tt1kn9v9 ай бұрын
Woaw just woaw..
@nieohneseifewaschenyoyoyo3440 Жыл бұрын
Kannst bitte mehr deutsche Videos machen :( das ist genau mein Thema und ich versteh kein Wort
@brightsideofmaths Жыл бұрын
Deutsche Videos veröffentliche ich dann auf dem deutschen Channel.