Not only 0 and 1 are Schelling points - default options you can assume pretty much everyone would chose - they're also special in the way that they define a (positive) range where numbers always stay inside that range under multiplication. Two numbers between 0 and 1 multiplied together will always give a number that's also between 0 and 1. That's why a lot of places in math like to transform domains into the 0...1 range.
This. Another way to express it is that for an interval [a, b], multiplying two numbers c, d within that interval will be within [aa, bb], and for 3 numbers [aaa, bbb], but it's super convenient to that for a=0 and b=1 these are always [0,1]. Other numbers would work, but would become cumbersome.
