Feedback | SoME

How to Construct Infinite Sets

What are the natural numbers? The integers? The rationals? The reals? While we may have an intuitive understanding of these numbers and sets, it is not so easy to actually construct these sets formally. To do so, we must use some axioms of set theory, and using only these assumptions, formally describe what these infinite sets should look like. We will develop various tools in set theory, like ordered pairs, relations, ordering, and equivalence classes, to begin with only zero, and from nothing, build all of the real numbers.

Analytics

5.66 Overall score*

54 Rank

22 Votes

6 Comments

Comments

Great animation and explanation of set theory. The most important thing that you absolutely nailed was that we are creating formal definitions of these infinites, there's no right answer.

8.6

This is a great video! I am especially happy to see that you explained what we are constructing is a set with the properties we want real numbers to have. That we are not constructing *the* real numbers, but rather a *model* of the reals in set theory, and that the value of such a construction is that it proves the tools of set theory can be used to “talk about” the real numbers. Most of the treatments I have seen on this topic—including in university-level courses—have conveyed the incorrect notion that these sets *are* the real numbers. So I am very glad to see your video correctly point out that these are *not* the real numbers, they are simply one possible way to construct sets which behave the way we want real numbers to behave. The real numbers *are* a collection of intuitive ideas about distance, which can be summarized in math jargon as “a complete, ordered, archimedean field”. The importance of constructions like the one in the video is to enable set theory to be employed in proving theorems about them. Well done!

1. Make sure you're looking directly at the camera when speaking! 2. Make the motivation at the beginning of the video stronger. Why should the viewer care? 3. Have some sort of "preview" for what the video will talk about

6.9

Quite detailed, engaging music, proper narration.

Very well animated and presented. Visual proofs for abstract concepts which are well introduced in video. Fascinating area and rigorous/uses formal language.

I think the length of the video is little bit excessiv, and the music is a little bit distracting otherwise its a really great and well produced video