I wouldn't say they don't mean the usual numbers 0 and 1 in this setting. F_2, also called GF(2) in another standard notation, can readily be interpreted as the set containing only the natural numbers 0 and 1, together with the operations of addition modulo 2 and multiplication. In other words, everything has its usual meaning, except that addition wraps around so that you remain in the two-element set.
Finite fields are kind of fun. The body of knowledge about them is called Galois Theory and makes a pretty good entrée into the world of abstract algebra. Interested readers might want to check out the short, $8 book by Émil Artin from Dover [0] for a good introduction.
Finite fields are kind of fun. The body of knowledge about them is called Galois Theory and makes a pretty good entrée into the world of abstract algebra. Interested readers might want to check out the short, $8 book by Émil Artin from Dover [0] for a good introduction.
0. https://www.amazon.com/Galois-Theory-Delivered-University-Ma...