From Wikipedia:
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Originally Posted by The Full Stop
Many descriptivists (i.e. people who describe how language is used in practice) support the notion that a single space after a full stop should be considered standard because it has been the norm in mainstream publishing for many decades. This also includes the MLA, APA, and the CMS. Many prescriptivists (i.e. people who make recommendations for rules of language use), meanwhile, adhere to the earlier use of two spaces on typewriters to make the separation of sentences more salient than separation of elements within sentences. Some, however, accept that in modern word-processing the single space is better because two spaces may stretch inordinately when full justification is applied. Additionally, many computer typefaces are designed proportionately to alleviate the need for the double space (the opposition would of course reply that this does nothing to satisfy the aforementioned saliency issue). Most modern typesetters, designers, and desktop publishers use only one space after a period, as do most mainstream publishers of books and journals.
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It really boils down to the fact that in professional typesetting, a full stop was the width of 1.5 spaces. On a typewriter, or when using a monospaced typeface, the best approximation of a full stop would have been two single spaces. Modern word processers with proportional fonts can correctly render the 1.5 space full stop after a period, so the use of a "double space" is unnecessary.
There's nowhere I can't reach.