Mimimum and Minimal element of an ordered set

Question

During study of ordered sets,I gone through 'minimal element' and 'minimum element' of a set. Can someone explain the difference between them with examples?

Many thanks and regards,

Answer 1

Minimum: minimum is an element that is less than all other elements of the set.

Minimal: minimal is an element such that there is no element less than that.

Here are some observations that may help:

• The main difference between these two is that minimal cannot be compared with all the elements of the set. However, among those that can be compared to is minimum

• Minimum is an element that can be compared to all the elements of the set and is less than all of them.

• Each minimum need to be minimal but the reverse is not true.
• There may be several minimals in a set while minimum is always unique.