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What is the general difference between the words 'rest' and 'remainder'?

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    Both (taking just the relevant homonym of rest) have quite a few meanings; 'remainder' has some rather more specialist senses. Looking at just one situation where there is an obvious choice: The rest of the day is the normal, unmarked expression. The remainder of the day sounds either more formal or serious - or just more pretentious. Care should be taken to keep to Orwell's second rule unless one has a good reason not to. Perhaps 'the remainder of the holidays' and 'the rest of the holidays' suggest different things - one week remaining, and three occasional days left this year. – Edwin Ashworth Sep 27 '13 at 8:32
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    The only difference is that lawyers like to use them both in special phrases like the rest, residue, and remainder, just in case there might be some differnence. – John Lawler Sep 27 '13 at 16:38
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The word "remainder" can be used as a synonym for "rest" ("We finished the remainder of last night's stew"). However "remainder" also has certain specific meanings, and is more commonly used in those contexts.

Math: the leftover portion following a division operation. 43 divided by 10 equals 4 with a remainder of 3.

Publishing: a book sold at a discount (usually a work that's losing popularity).

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We rest in bed, and remain in bed, but we do not remainder in bed. A seller of goods can sell the rest or the remainder, but a seller of services can do neither. We can offer the rest of something or equally offer the remainder of the rest.

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