reply to post by imdateach
Well, if you like math, you could figure which two numbers come after 2 and 3.
One would say that there is nothing much to figure, because if 2 and 3 are interpreted as primes, then after 2 and 3 comes 5 and 7. The problem is the
word IF. What if 2 and 3 were not taken from the series of primes and both numbers represent something else? For example, if 2 and 3 are positive
integers, as they truly are, then after 2 and 3 comes 4 and 5.
It follows that whatever comes after 2 and 3 depends on the description of both numbers. That also applies to the case where any two numbers have some
special property, as it is the case with 2 and 3.
The special property of 2 and 3 starts this way: If you keep dividing 2 by 3, the result is a one number that keeps repeating.
2 / 3 = 0.666666666666666666666666666...
(When you get tired of repeating the procedure and suspect that there would be no change in the repeating pattern, you stop and end the result with
ellipses (...) to indicate that the sixes will repeat ad infinitum.)
Obviously dividing 2 by 3 takes too much time -- there are just too many sixes to deal with, especially when a person needs just one six. Since
division is the opposite to
multiplication and
many is the opposite to
a few, it follows that multiplying 2 by 3 should
produce only a few sixes. Let's see . . .
2 x 3 = 6
Here we go. There is only one six in the result.
Are 2 and 3 special numbers in this respect, or are there any other two numbers A and B apart from 2 an 3 where
A / B = 0.CCCCCCCCCCC... and A x B = C ?
This question could be expanded to the case of a repeating group of digits, like in the case of 1 / 7.
1 / 7 = 0.142857 142857 142857 ... ...
In this case, the generalized question asks if
A / B = 0.REPEAT ... ... and A x B = REPEAT.
I actually didn't try to figure this out, so I'm curious if there are any numbers A and B like that apart from 2 and 3.