Characteristics of Floor and Ceiling Function/Real Domain/Historical Note
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Historical Note to Characteristics of Floor and Ceiling Function: Real Domain
The limitation of Characteristics of Floor and Ceiling Function to rational numbers was demonstrated by Georg Karl Wilhelm Hamel in $1905$.
Sources
- 1905: Georg Hamel: Eine Basis aller Zahlen und die unstetigen Lösungen der Funktionalgleichung: $\map f {x + y} = \map f x + \map f y$ (Math. Ann. Vol. 60: pp. 459 – 462)
- 1997: Donald E. Knuth: The Art of Computer Programming: Volume 1: Fundamental Algorithms (3rd ed.) ... (previous) ... (next): $\S 1.2.4$: Integer Functions and Elementary Number Theory: Exercise $49$: Answers to Exercises