Complete and Bounded Lattice

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Discrete Mathematics: Complete and Bounded Lattice
Topics discussed:
1) Definition of complete lattice.
2) Examples of complete lattice.
3) Definition of bounded lattice.
4) Examples of bounded lattice.
5) Properties of bounded lattice.

Music:
Axol x Alex Skrindo - You [NCS Release]

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

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

rajeshprajapati
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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?

JB-knzh
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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.

saranshvats
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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

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

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

niranjanreddykarri