Science Memes

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submitted 4 months ago by [email protected] to c/[email protected]

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[–] [email protected] 26 points 4 months ago* (last edited 4 months ago) (2 children)

ok, I define 1 as {∅} and 2 as {∅, {∅}}

proving the addition holds is slightly more complicated

[–] Wilzax 12 points 4 months ago (2 children)

Now define "+"

[–] [email protected] 32 points 4 months ago (1 children)

I love the comment that it's "occasionally useful"

[–] Wilzax 15 points 4 months ago (1 children)

Hmm yes.. set theory... I don't understand anything happening here

[–] [email protected] 12 points 4 months ago* (last edited 4 months ago) (1 children)

There is actually a really good explanation for us math-curious non-mathematicians here:
https://blog.plover.com/math/PM.html

[–] [email protected] 3 points 4 months ago

That's some good read, thank you so much.

[–] [email protected] 8 points 4 months ago (2 children)

+ is a map from N×N to N where a + 0 = a and a + 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.

[–] [email protected] 4 points 4 months ago (1 children)

seems a little sus to use + to define +

[–] apolo399 9 points 4 months 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."

is just a symbol. You could instead write it as +(a,0)=a and +(a,S(b))=S(+(a,b)).

You have to have previously defined 1=S(0), 2=S(1), 3=S(2), and so on.

[–] porl 4 points 4 months ago* (last edited 4 months ago) (1 children)

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. https://youtube.com/@anotherroof

Here is a playlist of the topic: https://youtube.com/playlist?list=PLsdeQ7TnWVm_EQG1rmb34ZBYe5ohrkL3t

[–] [email protected] 2 points 4 months ago

ooh, that looks interesting!