Eighty years (there was no 'year zero' !).
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58 years are between 30 BC and AD 30. The first thing you need to remember is that there is no year 0; the year before AD 1 is 1 BC. So the years between 30 BC and AD 30 are... 29 BC, 28 BC, 27 BC, ..., 2 BC, 1 BC, AD1, AD 2, ..., AD 27, AD 28, AD 29 29 BC through 1 BC is 29 years, and AD 1 through AD 29 is 29 years. 29 years + 29 years = 58 years
There are 19 years between 10 BC and 10 AD. The reason for this is that there is no year 0 in the Gregorian calendar system, so the year following 1 BC is 1 AD. Therefore, you need to count from 10 BC to 1 AD (10 years) and then add the 9 years from 1 AD to 10 AD, totaling 19 years.
The years between 27BC and 69 AD is 96 Years.
Yes. The simple answer is that rational fractions are infinitely dense. A longer proof follows:Suppose you have two fractions a/b and c/d where a, b, c and d are integers and b, d are positive integers.Without loss of generality, assume a/b < c/d.The inequality implies that ad < bc so that bc-ad>0 . . . . . . . . . . . . . . . . . . . (I)Consider (ad + bc)/(2bd)Then (ad+bc)/2bd - a/b = (ad+bc)/2bd - 2ad/2bd = (bc-ad)/2bdBy definition, b and d are positive so bd is positive and by result (I), the numerator is positive.That is to say, (ad+bc)/2bd - a/b > 0 or (ad+bc)/2bd > a/b.Similarly, by considering c/d - (ad+bc)/2bd is can be shown that c/d > (ad+bc)/2bd.Combining these results,a/b < (ad+bc)/2bd < c/d.
739 BC happened 739 years before the birth of Christ, and 465 AD happened 465 years after his death.