The point is not that you can represent it better. The point is that you can actually run it. You can't run the original notation (as such, we know languages that are close, of course).
I agree that the terser notation is better if you're just considering the mathematics in isolation. However, I also think that the true power of this kind of mathematics isn't made evident to people until you actually add some integers and make some lists.... from "nothing"... in a language you already know.
It's the same reason he doesn't use lisp or haskell, which are, obviously, vastly more appropriate. The idea is to illustrate something using something people have readily at hand. Once you have the concrete representation of the idea, you can work backwards to whatever notation you desire and forwards again using that notation, understanding that, yes, it has a basis in reality.
It's the same reason people draw 2d graphs to represent machine learning concepts instead of solely relying upon linear algebra notation. Humans are limited in that way: we have to gain some kind of appropriate intuition, and then we can work with the abstractions after that. No one is going to argue that js is an appropriate way to develop the mathematics -- it's just a way to make it more concrete for people, that's all.
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The point is not that you can represent it better. The point is that you can actually run it. You can't run the original notation (as such, we know languages that are close, of course).
I agree that the terser notation is better if you're just considering the mathematics in isolation. However, I also think that the true power of this kind of mathematics isn't made evident to people until you actually add some integers and make some lists.... from "nothing"... in a language you already know.
It's the same reason he doesn't use lisp or haskell, which are, obviously, vastly more appropriate. The idea is to illustrate something using something people have readily at hand. Once you have the concrete representation of the idea, you can work backwards to whatever notation you desire and forwards again using that notation, understanding that, yes, it has a basis in reality.
It's the same reason people draw 2d graphs to represent machine learning concepts instead of solely relying upon linear algebra notation. Humans are limited in that way: we have to gain some kind of appropriate intuition, and then we can work with the abstractions after that. No one is going to argue that js is an appropriate way to develop the mathematics -- it's just a way to make it more concrete for people, that's all.