Arithmetic progression notation

Arithmetic progressions are one of the most fundamental structures in mathematics. However, their representation in standard form often becomes lengthy and repetitive, especially when dealing with general terms or finite index bounds. This paper introduces a compact operator notation, written as ω[α1→αi], that clearly encodes the structure of a finite arithmetic progression using minimal symbols. The notation simplifies expression, improves readability, and supports algebraic operations relevant to further research in number theory.