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In recreational mathematics, an almost integer (or near-integer) is any number that is not an integer but is very close to one. Almost integers may be considered interesting when they arise in some context in which they are unexpected.
An almost integer is a number that is very close to an integer. Near-solutions to Fermat's last theorem provide a number of high-profile almost integers.
The reason that this $j$-value is an integer is due to the quadratic field $\mathbb{Q}(\sqrt{-163})$ having class number one, or equivalently that all positive-definite integer binary quadratic forms of discriminant $-163$ are equivalent.
In most cases, almost integers exist merely as numerical coincidences, where the value of some expression just happens to be very close to an integer. However, sometimes there actually is a clear, mathematical reason why certain irrational numbers should be very close to whole numbers.
Oct 30, 2012 · Almost integers (or near integers [1] [2]) are numbers which, although not being integers on account of having a fractional part, are very close to integers and can be mistaken for such as the result of a loss of machine precision during a calculation.
They are algebraic integers of degree $2$, but they are also almost integers themselves. The same phenomenon happens with Class $2$ numbers $88$ and $148$. Is there another modular function that explains why these numbers are almost integers?
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Mar 1, 2019 · Informally speaking, an "almost integer" is a real number very close to an integer. There are some known ways to construct such examples in a systematic way. One is through the use of certain algebraic numbers called Pisot numbers.
