Now, in Bitcoin, I'm thinking of a number between one and 2^160 (in fact, it's a little less, but let's not delve into technical details too much).
a good analogy with the "guessing the number" thing, but there is a tiny mistake here. that "number" that we choose in bitcoin (aka private key) is between 1 and a little less than 2
256 then that number is "converted" and "compressed" using one way operations to a smaller size (2
160).
in other words when someone is guessing the number they still have to perform those two time consuming operations to a get a result and compare it with yours.