Early computer installations were designed only to support a single writing system, typically for the Latin alphabet only. Adding new character sets and character encodings enabled a number of other left-to-right scripts to be supported, but did not easily support right-to-left scripts such as Arabic or Hebrew, and mixing the two was not practical.
With bidirectional script support, it is possible to mix scripts from different languages on the same page, regardless of writing direction. In particular, Unicode provides complete BiDi support, with detailed rules as to how mixtures of left-to-right and right-to-left languages are to be encoded and displayed.
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