How to prove that every minimum of a poset is a minimal element?

[codercat]

Hi! I am supposed to prove that a minimum of a partially ordered set is also the minimal element of that set.

It seems simple enough, I just don't really know how to formally prove this.

The poset is reflexive, anti-symmetric and transitiv.

A minimum is the unique least element of the set, the minimal element is not unique.


Could someone help me solve this? Thank you!

 

[Dr.Peterson]

Hi! I am supposed to prove that a minimum of a partially ordered set is also the minimal element of that set.

It seems simple enough, I just don't really know how to formally prove this.

The poset is reflexive, anti-symmetric and transitiv.

A minimum is the unique least element of the set, the minimal element is not unique.


Could someone help me solve this? Thank you!

Please quote the definitions, and the problem, exactly as given to you. What you say doesn't sound quite right. Precision is important here!

Once you get the wording right, it should be easy.