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The Halving was the phenomenon which caused everything in the Halfworld to exist only as a lower half, yet be able to function as if it were complete.
The Szaclowk, the Halfworld's sentient inhabitants, believed that the Halving had been a voluntary process undergone by their ancestors, who cast out their unworthy other halves. However, the Crew of the Copper-Colored Cupids did not lend much credence to this mythological theory, noting how everything else in the Halfworld had also been Halved, not just the Szaclowk. The Department of Cutlery believed that the Halving had been effected by a Cosmic Cleaver, while the Department of Mathematics argued for the “Ultimate Fraction Interpretation”. (PROSE: The Szaclowk & the Halfworld (short story)