This link has been bookmarked by 29 people . It was first bookmarked on 14 Jul 2006, by Jay Dugger.
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A familiar use of modular arithmetic is in the 12-hour clock, in which the day is divided into two 12-hour periods. If the time is 7:00 now, then 8 hours later it will be 3:00. Usual addition would suggest that the later time should be 7 + 8 = 15, but this is not the answer because clock time "wraps around" every 12 hours; in 12-hour time, there is no "15 o'clock". Likewise, if the clock starts at 12:00 (noon) and 21 hours elapse, then the time will be 9:00 the next day, rather than 33:00. Because the hour number starts over after it reaches 12, this is arithmetic modulo 12. According to the definition below, 12 is congruent not only to 12 itself, but also to 0, so the time called "12:00" could also be called "0:00", since 12 is congruent to 0 modulo 12.
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03 Sep 14
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In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus.
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04 Mar 14
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Time-keeping on this clock uses arithmetic modulo 12.
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congruence relation on the integers
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congruent modulo n,
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Jay DuggerModular arithmetic (sometimes called modulo arithmetic, or clock arithmetic) is a system of arithmetic for integers, where numbers "wrap around" after they reach a certain value — the modulus.
arithmetic math mathematics wikipedia wiki modular rings group theory
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