Talk:Partial algebra
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Partial
[edit]In a revealing passage Bernard Neumann introduced a "partial n-ary operator" and a "full n-ary operator" toward defining algebra in his presentation of universal algebra.
- B. H. Neumann (1961-62) Special Topics in Algebra: Universal Algebra, page 23, Courant Institute of Mathematical Sciences
He concedes, "This is a misuse of language – an adjective ought to specialize the object qualified, -- but it is more convenient to do it this way round." By way of explanation, he says "Full operators are much more important, and in the future we will probably drop the 'full' ". Rgdboer (talk) 23:39, 3 June 2026 (UTC)
Since an operation (mathematics) on a set is presumed to produce a set member for whatever arguments are presented to it, an operation is total. The adjective partial is a privative adjective which causes the reader some linguistic coercion to give the phrase meaning. In a context of conservative mathematics such adjectives are suppressed, or as Neumann says, a "misuse of language". However, contributors to universal algebra embraced the notion in the 1960s as a frontier of research. Ultimately, some authors realized that relational system (universal algebra) avoided the trap of describing the usual operations as total partial operations. — Rgdboer (talk) 22:46, 24 June 2026 (UTC)