adjoin

present singular third person adjoins · participle present adjoining · participle past adjoined · past adjoined

1. ambitransitiveTo share a common boundary or border with; to be physically contiguous to (a piece of land or property).

   The living room and dining room adjoin each other.

   3 more examples

   It's at this point that these three neighbourhoods adjoin.

   '[…] The land was so very desirable for me in every respect, so immediately adjoining my own property, that I felt it my duty to buy it. […]'

   1811, [Jane Austen], chapter XI, in Sense and Sensibility […], volume II, London: […] C[harles] Roworth, […], and published by T[homas] Egerton, […], →OCLC

   We were in the living area, which adjoins the kitchen.

   2013, Graeme Simsion, The Rosie Project, →ISBN, page 55

2. transitivealgebraTo extend an algebraic object (e.g. a field, a ring, etc.) by adding to it an element not belonging to it and then ensuring closure, for example by also adding all finite power series of the element.

   The field adjunction #92;mathbb#123;Q#125;(#92;pi) can be obtained from #92;mathbb#123;Q#125; by adjoining #92;pi to #92;mathbb#123;Q#125;.

   1 more example

   The ring adjunction #92;mathbb#123;Q#125;#91;#92;sqrt#123;2#125;#93; can be obtained from #92;mathbb#123;Q#125; by adjoining #92;sqrt#123;2#125; to #92;mathbb#123;Q#125;.