21. The dual number gradually disappeared from Aramaic over time and has little influence in Middle and Modern Aramaic. 22. Modern Dual number : Slavic languages for a discussion of number phrases in Russian and other Slavic languages. 23. With this description, it is clear that the dual numbers form a commutative ring with Division " ). 24. The algebra of dual numbers is isomorphic to the exterior algebra of \ mathbb { R } ^ 1. 25. Junction 8 / 9 at Maidenhead, Berkshire, is the only one in the UK with dual numbers . 26. Both declensions derive from the Indo-European dual number , otherwise defunct in Latin, rather than the plural. 27. Liouville's theorem does not extend to the generalizations of complex numbers known as double numbers and dual numbers . 28. Pseudo-Euclidean geometry is supported by alternative complex planes where points are split-complex numbers or dual numbers . 29. The special case of n = 1 is called a dual number , and was introduced by William Clifford in 1873. 30. The Baltic languages also used to have a dual number system, but it has become practically obsolete in modern Latvian and Lithuanian.
