Something you see very often but in different instances.
Once you recognize the notion, you see it almost everywhere.
| Numbers | Set Theory |
|---|---|
| \(\mathbb{N}\): \((+,0)\) | Semigroups |
| \(\mathbb{Z}\): \((+,0,\times,1)\) | Rings |
| \(\mathbb{Q}\) | Fields |
| \(\mathbb{R}\) | Complete Fields (topology) |
| \(\mathbb{C}\) | Algebræ |
| Modules,Vector Spaces, Monoids, ... |
More general: more things are sets.
& More precise: clear distinction between concepts)
| Numbers | Set Theory (\(\infty\)) | Category Theory (relations) |
|---|---|---|
| \(\mathbb{N}\): \((+,0)\) | Semigroups | ? |
| \(\mathbb{Z}\): \((+,0,\times,1)\) | Rings | ? |
| \(\mathbb{Q}\) | Fields | ? |
| \(\mathbb{R}\) | Complete Fields (topology) | ? |
| \(\mathbb{C}\) | Algebræ | ? |
| Modules,Vector Spaces, Monoids, ... | ? |
More general: more things are sets.
& More precise: clear distinction between concepts)
More general & more precise
Some math \(\sum_{i=1}^\infty \frac{1}{2^x} = 1 \)
Another math formula $$\sum_{i=1}^\infty \frac{1}{2^x} = 1$$
import Control.Monad
main :: IO()
main = do
putStrLn $ "Hello !"
/
#