Complete and Bounded Lattice

[@prabhk7258]

You are the best. Thank you so much for the effort and videos.

[@ashu3128]

Thank you,sir!!♥️

[@shaifalisinghgehlot2167]

I appreciate your hard word

[@dr.m.sundarmathematics5885]

Thank you. Slow and steady explanation

[@rajeshprajapati6662]

08:46 Supremum = Least Upper Bound = Join = Denoted by this symbol (∨). Also, Infimum = Greatest Lower Bound = Meet = Denoted by this symbol (∧).

[@vedantjoshi8176]

Thx for your effort

[@shivanikj3047]

Thank you 😃

[@tobelorne]

thank-_-you sir

[@eaglestargamer4813]

4:01 shouldn’t least upper bound x ?

[@saranshvats3833]

We have several finite lattices which are not complete. 1. 2. \. /. \./. 3. Here for (1,2) we don’t have LUB. So, finite lattice may be not complete. Also in this example it is finite but for (1,2) we don’t have upper bound too. So, finite lattices may not have upper bounds or lower bounds.

[@JB-kn2zh]

Maybe I'm confused, but isn't what you sketched out here not even considered to be a lattice? If (1,2) don't have an LUB, then it isn't a lattice. That's the definition of lattice, right?

[@anupamjha1742]

12 4. 6 2. 3 1 Divisibility relation Subset is {1,4,6} Then for thus subset no lUB exist

[@jeemantra7835]

first of all this hesses diagram is not a lattice

[@kulkarnisoham]

It isn't a littice in first place

[@JB-kn2zh]

So wait is a complete lattice basically the same thing as a bounded lattice, except it excludes empty relations, whereas an empty relation would still be considered to be a bounded lattice?

[@ayushrastogi7965]

Sir but greatest lower bound of f and b is a because first time they meet at a so a is the greatest lower bound of f and a

[@anfauglit]

No. _b_ and _f_ are related elements and _b_ is less than _f,_ therefore _b_ is the greatest lower bound of the set *{f, b}.*

[@EllenRipley1979]

Is there an infinite lattice that is complete? If so, what is it?

[@snehalsha4051]

No there can't be, because for ........-2 -1 0 1 2 3 -2 doesnt have glb 1 2 3 4......... 4 doenst have lub ....-1 0 1 2 3 ..... 3 doesent have lub (and -1 no lub) all 3 possibilities lead to incompleteness

[@madhurashanbhag9317]

There is. If we take 0 as the LB and 1 as the GB and all the real numbers between them which is essentially infinite between them, then that lattice though infinite will be both bounded and complete, because any subset will always have meet as 0 and join as 1.

[@madhurashanbhag9317]

@@snehalsha4051 you are only considering infinite chain lattices in your example, they are not the only infinite lattices, they are SOME of the not complete lattices.

[@optimist_ic]

​@@madhurashanbhag9317it says aaaalll of the subsets must have GLB and LUB

[@niranjanreddykarri9222]

Every non-empty finite lattice is not a complete lattice!

[@Mayankcodezz]

impresivezzz

[@snehalsha4051]

KTU ondo?