The Principles of Mathematics, Volume 1

adjectives aggregate analysis argument Arithmetic assertion asymmetrical relation axiom axiom of Archimedes belongs called Cantor cardinal number Chapter class of classes class of terms class-concept collection compact series complex concept concerning considered constituents contained contradiction correlation defined definition denoted discussion distance distinction distinguished entities equal equivalent existence fact false finite integers finite number follows formal implication Frege Geometry greater and less Hence hold identical implies indefinable infinite classes infinite wholes infinitesimal infinity kind of magnitude Leibniz limit logical constants logical product material implication mathematical induction means notion null-class number of terms object obtained one-one relation ordinal Peano philosophical pleasure points possible predicate present presupposed principle projective Geometry properties propositional function prove quantities question rational numbers real numbers regard seems segments sense similar single term Socrates space stretch supposed Symbolic Logic theory transfinite transfinite cardinals transitive relation true unity values variable zero