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Gamma is the name of Γ γ, the third letter of the Greek alphabet, approximately corresponding to G. The Greeks borrowed the letter names from the Phoenicians together with the alphabet, and in that sense the Greek name "gamma" is a cognate of, among others, Hebrew gimel and Arabic djeem.
Gamma rays is a name given to the shortest and most energetic electromagnetic radiation, and like all electromagnetic radiation they can exhibit wave-like or particle-like behaviour. However, since their actual definition depends on context more than on frequency or energy, there is some overlap between low-energy gamma rays and high-energy X-rays.