Talk:Associative Composition Algebra/Binarions

Discussion for Binarions:

Complex binarions may also be designated bibinarions since they are derived by raising the division binarions to the binary level. This coinage is a linguistic deduction in the language of composition algebras. Thus bibinarion joins bicomplex number and tessarine as an alternative label for a complex binarion. _ Rgdboer (discuss • contribs) 02:01, 28 December 2017 (UTC)

Ambiguity of "complex"
Already in 1903 Bertrand Russell expanded the meaning of complex number to the notion of a linear span in a vector space: "Let n different entities $$e_1, e_2, \dots e_n$$ which may be called elements or units be given, and let each be capable of association with any real number ... In this way entities $$\alpha_i e_i$$ where &alpha;i is a number... Then the combination, which may be written
 * $$a = \alpha_1 e_1 \ + \ \alpha_2 e_2 + \alpha_3 e_3 \dots \alpha_n e_n$$

is a complex number of the nth order." The Principles of Mathematics page 378

In the composition algebra context the term division binarions has been used instead, and division binarions are the only binarions that form a field. The prefix bi- in the context of this book refers to first level of Dickson doubling  of a field, so Bibinarions, as suggested above, serves a a unique designator and liberator from the  carry-over of "complex" in some coverage of the  algebra. Ambiguous terms may be replaced by more definite designations. Rgdboer (discuss • contribs) 03:10, 2 October 2021 (UTC) Rgdboer (discuss • contribs) 03:14, 2 October 2021 (UTC) Rgdboer (discuss • contribs) 03:20, 2 October 2021 (UTC) Rgdboer (discuss • contribs) 00:06, 6 February 2023 (UTC)