Omega (Ω/ω): La última letra griega

• Omega (Ω/ω) is the 24th and last letter of the Greek alphabet.
• In the Greek numeric system, it has a value of 800.
• The uppercase letter Ω is often used in scientific and mathematical contexts.
• The lowercase letter ω is also employed across various fields.

History and Shape

• Omega originated from the letter "o" of alphabets used in some Greek cities.
• It was introduced to represent a long "o" sound, differentiating it from omicron (Ο/ο), which represented a short "o".
• The name "omega" literally means "large O" (ō mega).
• The uppercase Ω resembles an incomplete circle with an opening at the bottom.
• The lowercase ω has several typographical variations, resembling an open "w" or a curved "v" connected to a horizontal line.

Usage of the Uppercase Letter (Ω)

Physics

• In physics, Ω represents the ohm, the SI unit of electrical resistance.
• It is also used to denote solid angle.
• In particle physics, Ω is used as a symbol for omega baryons.

Mathematics

• In probability theory, Ω often denotes the sample space, representing the set of all possible outcomes of a random experiment.

Computer Science

• In computational complexity theory, Ω signifies the lower bound of an algorithm's growth rate (Big Omega notation).

Other Fields

• In biochemistry, Ω can represent the dihedral angle associated with the peptide bond.
• Omega is used as the symbol for the last rank or class in ordered classifications such as graduate class ranking.

Usage of the Lowercase Letter (ω)

Physics

• In physics, ω commonly represents angular velocity or angular frequency.
• It can also denote the weight of an object in mechanics.

Mathematics

• In mathematics, ω is used to represent the first transfinite ordinal number (the ordinality of the natural numbers).
• In number theory, ω(n) represents the number of distinct prime factors of n.
• In complex analysis, ω can denote a complex cube root of unity.
• In differential geometry, ω may represent a differential form.

Computer Science

• In computer science, ω is used in Big Omega notation, similar to the uppercase version, but with subtle differences in meaning related to algorithm analysis.

Linguistics

• In linguistics, ω represents the labiovelar approximant.

Other Fields

• In genetics, ω can represent the rate of non-synonymous substitutions in proteins.
• In finance, ω is sometimes used to represent elasticity.
• In cosmology, ω is used to represent the density parameter, a measure of the average density of matter and energy in the Universe relative to a critical value.

Common Expressions and Idioms

• "Alpha and omega" signifies the beginning and the end, derived from a phrase used in the Book of Revelation.
• It indicates completeness or the entirety of something.

Symbolism

• Because it is the last letter of the Greek alphabet, omega is often used to represent the end or the ultimate limit of a process or situation.
• The association is commonly seen in religious, philosophical, and even fictional contexts.