On Numbers and Games

aẞ assertion atomic weight born on day Chapter component games compute conjunctive compound corresponding defined definition diagram disjunctive compound disjunctive sum dyadic rationals edges Elwyn Berlekamp equal equation field finite number follows formula G and H game G generalise Grundy number Grundy's game Hackenbush heaps impartial games inductive inequalities infinite infinitesimal integer Kayles Left and Right Left option legal move long games misère play negative numbers Nim-addition Nim-heap Nim-sum nodes normal play number x obtain option of G ordinal numbers ordinal sum positive numbers Proof proper Class properties prove real numbers remote stars replace reversible moves rule second player win short game sign-expansion simpler simplest form simplest number small games square suppose suspense number THEOREM theory thermograph trominoes Welter function winning strategy zero