I really recommend the YouTube channel “Another Roof”. His first few videos were building up exactly this idea, as well as building up all the real numbers (possibly complex too if I’m remembering correctly). Sounds like a dry topic but he uses humour really well throughout. youtube.com/@anotherroof
Comment on 1 + 1
FiskFisk33@startrek.website 1 month ago
ok, I define 1 as {∅} and 2 as {∅, {∅}}
porl@lemmy.world 1 month ago
FiskFisk33@startrek.website 1 month ago
ooh, that looks interesting!
Wilzax@lemmy.world 1 month ago
Now define “+”
FiskFisk33@startrek.website 1 month ago
Image
I love the comment that it’s “occasionally useful”
Wilzax@lemmy.world 1 month ago
Hmm yes… set theory… I don’t understand anything happening here
FiskFisk33@startrek.website 1 month ago
There is actually a really good explanation for us curious non-mathematicians here:
blog.plover.com/math/PM.html
MBM@lemmings.world 1 month ago
+
is a map fromN×N
toN
wherea + 0 = a
anda + S(b) = S(a + b)
(S
is the successor function that gives the next number).Then
1 + 1 = 1 + S(0) = S(1 + 0) = S(1) = 2
.funkless_eck@sh.itjust.works 1 month ago
seems a little sus to use + to define +
apolo399@lemmy.world 1 month ago
No, it’s correct. You define the operation by it’s properties. It’s not saying that “a plus 0 = a” but "the result of applying the binary operation ‘+’ to any number with 0 should give the original number."
You have to have previously defined 1=S(0), 2=S(1), 3=S(2), and so on.