Thank you! I’m literally taking an elementary abstract algebra course in a few days and I’ve had a lot of trouble over the years trying to find a simple explanation for what “ well defined” means. This is a breath of relief.
Those are different concepts. A function is well-defined if every element of the domain goes to exactly one element of the codomain. A function is a bijection if every element of the codomain comes from exactly one element of the domain. They are sort of "mirror image" concepts you get by flipping the domain and codomain. All functions are well-defined (it's part of the definition of being a function), but not all functions are bijections.
Thank you Jake, however I am absolutely cooked this semester to a point far past that of no return. It is certainly over for me, this class is not even required for me I am just stupid.
I have a discrete math midterm in 4 days and this was the only explanation that finally made sense, thank you!!
You're welcome :) I hope your midterm goes well!
What I personally find helpful while this video is explained is to think about uniqueness and existence throughout
I’m taking discrete math and this is much more helpful than the textbook
Great video this concept makes so much sense now and you explained it without making me feel dumb lol, really appreciate it!
Thank you! I’m literally taking an elementary abstract algebra course in a few days and I’ve had a lot of trouble over the years trying to find a simple explanation for what “ well defined” means. This is a breath of relief.
You're welcome! I'm happy I could help.
professor, you teach in a very simple style, very useful. appreciate it :)
I am taking Topology for the first time and trying to review ideas
Jake thanks so much for this video - I'm in a discrete math class and this cleared up a lot of confusion.
Thanks for the video. It blew up a light of my brain.
Thanks for letting me know! That's nice to hear.
Sir wonderful keep uploading ur research works for us its really very very very superb and interesting! Ur fan and student from india 🙏👏😊
Very good explanation, professor.
Thank you. That's really nice of you to say.
sur i have a question ... is that the same meaning (purity of function ) and ( well defined )?
Good video! I would also mention that if the output is not in the co-domain it is not well defined.
Very well explained..simple and to the point. We look for more such videos.❤️ frm India
Thanks so much. It made me happy to read your comment.
bro just saved my life
Really helpful! Thanks!
Thank you so much sir. it really helped!
So, a bijective function is the same as a "well-defined" function? Or not necessarily ...
Those are different concepts. A function is well-defined if every element of the domain goes to exactly one element of the codomain. A function is a bijection if every element of the codomain comes from exactly one element of the domain. They are sort of "mirror image" concepts you get by flipping the domain and codomain. All functions are well-defined (it's part of the definition of being a function), but not all functions are bijections.
Sir when we say set as well defined
Thanks!
Thank you Jake, however I am absolutely cooked this semester to a point far past that of no return. It is certainly over for me, this class is not even required for me I am just stupid.
Simple and very helpful
Thanks! I appreciate that.
Thank you mate
Is well-defined implicit in a function?
Yes, it's part of the definition of a function.
Thank you lol!
that was great thanks :)!!
You're welcome and thanks for letting me know! :)
why don’t the textbooks explain it like this? the paragraph it had was gibberish
mathematics is the (careful) study of cartoons
Nice
Good