i haven't checked it thoroughly, but it looks like all the desired properties of boolean arithmetic are preserved when false = 0 true = [1] (i.e. the equiv

i haven't checked it thoroughly, but it looks like all the desired properties of boolean arithmetic are preserved when false = 0 true = [1] (i.e. the equivalence class of all n > 0) && = + || = * spelling it out: || / + (or): 0+0 = 0 0+[1] = [1]+0 = [1] [1]+[1] = [1] && / * (and): 0*0 = 0 0*[1] = [1]*0 = 0 [1]*[1] = [1] where [1] stands for "any nonzero number". (please let me know if i missed anything!) so natural numbers (quotiented by an equivalence relation) seem to work as a model for boolean arithmetic. and idk if we need more mathematical justification than "it works fine" EDIT: changed "integers" to "natural numbers", because 5 + -5 = 0 so the `[1]+[1] = [1]` property doesn't hold