Hi, your videos are a real joy to watch, thank you so much for all the effort! I just want to point out that some of the initial videos are not in the correct order in the Real Analysis playlist, this is the first misplaced video, it should probably be: Addition of Dedekind Cuts, then Field Axioms for Addition, then Additive Inverse and so on. Again, your videos are great, thank you!
Sir, thak you for your work. But I cant understand the notation of addition that u used in this video. alpha and beta are sets. So how do we add them? What does this addition mean?
@volkandemir6353 Since alpha and beta are Dedekind cuts, they are subsets of the rationals. We can define alpha+beta = {a+b| a \in alpha and b \in \beta} This will also be a subset of the rationals. We need to check that it is also a Dedekind cut and that it has all of the properties of the addition that we know and love! Great Question!
Yup! I write normally and then mirror the image when the video is produced! Hope you enjoy! I will post the multiplication axioms with Dedekind cuts later this week!
Hi, your videos are a real joy to watch, thank you so much for all the effort! I just want to point out that some of the initial videos are not in the correct order in the Real Analysis playlist, this is the first misplaced video, it should probably be: Addition of Dedekind Cuts, then Field Axioms for Addition, then Additive Inverse and so on. Again, your videos are great, thank you!
Thanks @yurimuniz1997 I definitely need to reorder them!
Sir, thak you for your work. But I cant understand the notation of addition that u used in this video. alpha and beta are sets. So how do we add them? What does this addition mean?
@volkandemir6353 Since alpha and beta are Dedekind cuts, they are subsets of the rationals. We can define alpha+beta = {a+b| a \in alpha and b \in \beta} This will also be a subset of the rationals. We need to check that it is also a Dedekind cut and that it has all of the properties of the addition that we know and love! Great Question!
@@mikethemathematician Wow, thanks for your quick answer. I appreciate your effort.
is this guy writing backwards?
ah nevermid I guess is mirrored on post haha
Yup! I write normally and then mirror the image when the video is produced! Hope you enjoy! I will post the multiplication axioms with Dedekind cuts later this week!