Surreal numbers as generalized Dedekind cuts

Two different surreal numbers $x,y$ are equal if $x\leq y$ and $y\leq x$, where that order is defined in terms of their recursive parts. So you can have $$2=\{1\mid\}=\{0,1\mid\}=\{1\mid4\}=\{-17,1.5\mid\pi\}$$

It's good to think of Dedekind cuts only as far as "Ah, we can use sets of relatively simple numbers to build more complex numbers", but not a lot further than that.