Almost integrity" does not depend on the number system. A number is called almost an integer if the distance from it to the nearest integer is small enough. Almost integers arise in the context in which they are unexpected which makes them interesting. A set of almost integers due to D. Hickerson is:
for , as summarized in the following table.
These numbers are close to integers due to the fact that the quotient is the dominant term in an infinite series for the number of possible outcomes of a race between people (where ties are allowed). A whole class of Irrational “almost integers'' can be found using the theory of Modular Functions, and a few rather spectacular examples are given by Ramanujan (1913-14). Such approximations were also studied by Hermite (1859), Kronecker (1863), and Smith (1965).
11.10.2021, 15:50 