## Nullifying Dichotomies

2023-11-06 | tags : dichotomy, knowledge representationIs it always possible to nullify a dichotomy? When tossing a coin, the outcome is either head or tail. However, head and tail are two faces of the same coin. In a sense, there isn't a split between head and tail as both belong to the same coin.

Let's try to think formally about this:

let `A`

and `B`

be two sets such that their elements follow distinct properties:

A={a | P(a)} , B={b | Q(p)}

A Dichotomy is the union of the two sets `D = A ⋃ B`

The dichotomy is nullified if a relation between `P(a)`

and `Q(b)`

exists.

The generation of a dichotomy can be synthesized as:

D = {a, b | p R q}