Yes, if the set is in such a way that, there is an element which is greater than or equal to all the elements in that set, then ya. For example, take the set {1,5,7,9} with relation "greater than or equal to" . It is well ordered, as 9 is greater than every other element. The main two conditions are: 1. The set S together with relation R, i.e (S,R) should be a Totally Ordered set. 2. Every non empty subset of S should have a least element with respect to the relation R. (For eg, element 'a' belonging to set S is a least element with respect to relation R, if aRb ,for all 'b' belongs to S.) If these two conditions are met, then it is well ordered.
Hello, does the least element need to be element of the subset or not ? And by the way, is the poset (Z+, |) a well ordered set ? I would say no because if I take the subset {2,3}, there is no least element. Am I right ? Thanks in advance.
Why do you think, that a subset of well ordered set need not be well ordered? If the statement "every subset of well ordered set is well ordered" was false, then, you can always show that by a counter example. Take a well ordered set, and take a subset of it, which is not well ordered. Then, you are done. But, I don't think the statement you mentioned is true. I think, every subset of a well ordered set is well ordered. Correct me, If am wrong. Anyway, to show every subset is also well ordered, showing examples won't work, that, you have to prove in general. Hope, I have made the point.
wonderful explaination
Found this video really helpful ! Good teaching style
Thank you! that's glad to hear!
Kudos to such explaination.
Commenting just to appreciate your way of explaination 😄
Thank you Rahul !
i understood it completely, thanks
To the point!perfectly understood this...thank you!
That's glad to hear. Thank you!
What does mean of least element i didn't understand
Fantastic video, good example that made it clear
Thank you!
what is the meaning of a totally ordered set?
Incredible! Thank you
Thank you
Great explanation 👏
Thank you
What if ‘greater than or equal ‘ to had a ‘finite set ‘ ,will it be well ordered
Yes, if the set is in such a way that, there is an element which is greater than or equal to all the elements in that set, then ya.
For example, take the set {1,5,7,9} with relation "greater than or equal to" . It is well ordered, as 9 is greater than every other element.
The main two conditions are:
1. The set S together with relation R, i.e (S,R) should be a Totally Ordered set.
2. Every non empty subset of S should have a least element with respect to the relation R. (For eg, element 'a' belonging to set S is a least element with respect to relation R, if aRb ,for all 'b' belongs to S.)
If these two conditions are met, then it is well ordered.
Hello, does the least element need to be element of the subset or not ? And by the way, is the poset (Z+, |) a well ordered set ? I would say no because if I take the subset {2,3}, there is no least element. Am I right ? Thanks in advance.
Firstly its not an totally ordered set because its elements are not comparable
sir, how to show that subset of a well ordered set need not be well ordered
Why do you think, that a subset of well ordered set need not be well ordered? If the statement "every subset of well ordered set is well ordered" was false, then, you can always show that by a counter example. Take a well ordered set, and take a subset of it, which is not well ordered. Then, you are done. But, I don't think the statement you mentioned is true. I think, every subset of a well ordered set is well ordered. Correct me, If am wrong. Anyway, to show every subset is also well ordered, showing examples won't work, that, you have to prove in general. Hope, I have made the point.
Hello sir...plz reply
Is there any proof of
'Every set can be well ordered '
en.wikipedia.org/wiki/Well-ordering_theorem
Super explain sir
Thank u so much sir, you are doing great job again many many thank u 🙏🙏🙏 sir🙏🙏🙏🙏🙏🙇🏼🙇🏼🙇🏼🙇🏼🙇🏼🙇🏼🙇🏼🙇🏼🙇🏼🙇🏼🙇🏼🙇🏼🙇🏼🙇🏼🙇🏼🙇🏼
Thank you!