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I stumbled across the fact that there are an infinite number of reciprocal pairs that share mantissas (meaning they are separated from their reciprocals by an integer). I thought it was worthy of inclusion. In fact, I haven't been able to find any information that this had already been discovered,
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but I don't really think I was the first. I'm also curious if the formula I found for identifying them, finds all such pairs. Can anyone direct me to a text or other source where this fact had already been discussed? I would appreciate reading more about it.
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a^(-1).a.(x-y)=0" should be deleted: the proof is supposed to show that a^-1 exists, so we can't use it in the proof. We can skip directly from line 2 to line 4 since a is not a zero divisor.
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https://s.yimg.com/hd/answers/i/3659d3369ebb4c4da9e17b1fb09b8d13_A.jpeg?a=answers&mr=0&x=1393291657&s=b8efbedb4fe036d7d231d0a0d08b5b8b
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the convoluted terminology 'multiplicative inverse' is preferred to 'reciprocal', even as early as the seventh grade:
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I see that there was in 2007 a stub article 'reciprocal' which might have dealt with this point.
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If the product rule is associative, it's easy to see that the two have to be the same -- eg, if
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Are there systems where one has to consider different left and right multiplicative inverses?
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In the "Further
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What can be said about the conditions for the right inverse and left inverse to be equivalent?
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The two still turn out to be the same if the algebra is not associative, but it is
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Does it hold generally for algebras constructed using the
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respectively, then associativity would seem to imply that
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Thsi equation has the right properties to be used in
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I'm not sure whether the equivalence still holds for
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