Mini Introduction to Dedekind Cuts

I love math and have been learning analysis by myself for about one year. I have tried to draw and briefly explain Dedekind cuts.

※PS: Thank you for the questions. I will try to answer them as best as I can. Further questions and comments are most welcome.
1. Why do you use one to construct the blue cut (on the second picture)?
A: We can use any rational number, and it will always be a cut.
2. Why does a cut not have a maximum?
A: Given any rational number in the cut, we can still find a slightly larger number that is still in the cut.
3. Why does finding the least upper bound (supremum) imply completeness?
A: Every cut is a real number. For any set of cuts that is bounded above, we can always find a cut, and thus a real number, that is the set's supremum. We cannot always do this with rational numbers.

Hello~ I am MeeMee GuLu, a homeschooled student in Taiwan. I care about the environment and love math.

[nyx]

in 4 minutes you explained more than my professor in 1 hr

[kashalasha]

yoo thank you for this the visuals really helped me understand!

[JhaaJii]

Great video mate! Keep it up. The donkey seems to be rather overenthusiastic though.