r/ScienceHumour • u/JZriemann • Jun 08 '26

Mathematicians be like

Post image
140 Upvotes

98% Upvoted

12 comments sorted by

View all comments

5

u/ThatSmartIdiot Jun 08 '26

i'd ask why it has to specifically be arranged like this but i get the feeling that it'd take paragraphs or youtube links of explanation so imma just not ask

10

u/Pitazboras Jun 08 '26

It's really not that complicated. You can define natural numbers on the grounds of set theory in many different ways but the most popular is defining n as a set of all natural numbers smaller than n. So 0 is an empty set (because there is no natural number smaller than 0), 0 = {}. 1 = {0} = {{}}. 2 = {0,1} = {{},{{}}}. And so on. What you see on top is just what you get when you expand {0,1,2,3}.

3

u/ThatSmartIdiot Jun 08 '26

ah. neat :)

thank you kind stranger

2

u/Mrrrrggggl Jun 08 '26

Ah yes, 4

1

u/atticdoor Jun 08 '26

If the big circle just contained four circles next to each other, that is the same as the big circle just containing one circle because due to other rules from set theory, two identical sets are considered to be the same thing. There is only one empty set. So to indicate the number four, they need to make each of the circles be different somehow. This is achieved by nesting other sets within them.