1. Hasse diagram (doubt)

In the attached diagram...

How come lower bounds of {15,45} are 3, 15, 5 and why not only 3, 5.
Why is "15" there in the lower bound? Why should it be there?

2. Originally Posted by robocop_911
In the attached diagram...

How come lower bounds of {15,45} are 3, 15, 5 and why not only 3, 5.
Why is "15" there in the lower bound? Why should it be there?
Because 15|15
It's the minimum of the set {15,45} and thus it belongs to the set of lower bounds.

3. Originally Posted by Moo
Because 15|15
It's the minimum of the set {15,45} and thus it belongs to the set of lower bounds.
So, is it so that the minimum of the set should also be taken into lower and upper bounds?

4. Originally Posted by robocop_911
So, is it so that the minimum of the set should also be taken into lower and upper bounds?
When it exists, yes.

Because most of the time, you won't have a minimum.
If you had to study {24, 45} for example, there is no minimum, but there is a set of lower bound(s), which is... ?

Imagine you had the set {3; 45}, would you say there is no lower bound ? There is, and it's 3

5. Originally Posted by robocop_911
So, is it so that the minimum of the set should also be taken into lower and upper bounds?
Yes, as long as the definition of your operator is satisfied.