logic is what we call for statements that we assume to be true without proofs.
logic is what we call for statements that we assume to be true without proofs.
what do we call statements that we assume to be true without proofs?
logic
statements such as "any two lines in a plane meet" are called "incidence propositions". this particular statement is true in a projective plane, though not true in the euclidean plane where lines may be parallel. historically, projective geometry was developed in order to make the propositions of incidence true without exceptions, such as those caused by the existence of parallels. from the point of view of synthetic geometry, projective geometry "should be" developed using such propositions as axioms. this is most significant for projective planes due to the universal validity of desargues' theorem in higher dimensions.
incidence (geometry)
the term a-group was probably first used in , where attention was restricted to soluble a-groups. hall's presentation was rather brief without proofs, but his remarks were soon expanded with proofs in . the representation theory of a-groups was studied in . carter then published an important relationship between carter subgroups and hall's work in . the work of hall, taunt, and carter was presented in textbook form in . the focus on soluble a-groups broadened, with the classification of finite simple a-groups in which allowed generalizing taunt's work to finite groups in . interest in a-groups also broadened due to an important relationship to varieties of groups discussed in . modern interest in a-groups was renewed when new enumeration techniques enabled tight asymptotic bounds on the number of distinct isomorphism classes of a-groups in .
a-group