Let \(b \ge 2, k\ge 0\) be natural numbers. A \(b\)-adic fraction is a real infinite series of the form
\[\pm \sum_{k=-n}^\infty a_kb^{-k},\]
where for all \(0\le a_k < b \) for all \(k\). The number \(b\) is called the basis or the radix of the \(b\)-adic fraction.
If the basis is known, we can write the b-adic fraction also explicitly in the form
\[\begin{array}{rcl} \pm a_{-k}a_{-k+1}\cdots a_{-1}a_{0} & . & a_{1}a_{2}a_{3}\cdots \\ &\uparrow&\\ \end{array}\]
The dot in the middle denotes the position of the \(0\)-th element of the sequence.
Chapters: 1
Definitions: 2
Proofs: 3
Propositions: 4 5
