lattice

Question

What is difference between finite lattice and bounded lattice?

plz give informal definition

Comments

 Ashwin Kulkarni  sir plz check this one 

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every finite lattice is bounded.

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If upper bound and lower bound of lattice exists then it will be bounded lattice.

for eg, [{1,2,3,4} <=}] this is chain on which upper bound 4, lower bound 1 exists.

Also [D18,/] is also a bounded lattice.

 

As per @Anu sir said, every finite lattice is a bounded lattice.

Answer 1

Every finite lattice is a Bounded lattice because for any Finite lattice, We can Prove that It has a least as well as a greatest element. 

Every finite lattice is a Bounded lattice But the Converse is not true. i.e. A Bounded lattice may or may not be Finite. For example, $\left ( \left [ 0,1 \right ], \leq \right )$ is a Bounded lattice but Not finite. Here the least element is 0 and greatest element is 1.

Note that $\left ( \left ( 0,1 \right ), \leq \right )$ is Not Bounded lattice because there is No least or greatest element.

Comments

This is finite lattice but not bounded, because (a,b) doesn’t have a greatest upper-bounded and (f,g) doesn’t have a greatest lower bound.
Hence your statement

“ Every finite lattice is a Bounded lattice ” is wrong!!!

Correct me if I am wrong.

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This is finite lattice

 @crackca ,

The Hasse diagram that you have given, does not represent a lattice.

In a lattice, every two elements have LUB, GLB.

Watch the discrete mathematics lectures below (only sign in required) for understanding all the concepts clearly and with proofs, without by-hearing anything.

https://www.goclasses.in/s/store/courses/description/Discrete-Mathematics