To represent the usual natural numbers, one could use the following sets

At first, this seems quite sensible. But it turns out to be very akward. For instance, how could we define $n < m$ for $n$ and $m$ natural numbers defined as above? Perhaps saying that one has more curly braces than the other one? That's no good. Instead, we'll proceed as follows:

Clever, isn't it? Now we would have $n < m$ if and only if $n\in m$. But in fact, it's more than that, because this pattern will appear again with ordinal numbers