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 help with a distributivity law JmsNxn Long Time Fellow Posts: 291 Threads: 67 Joined: Dec 2010 09/22/2011, 03:32 PM (This post was last modified: 09/22/2011, 03:43 PM by JmsNxn.) Yes I saw the little mistake I made where I assumed $f(0) = 1$. The reason is because I've only really been observing functions which meet that requirement. I think I'm not doing anything inconsistent but instead we have to create the law, which is not dissimilar to division by zero: $f(0)\,\otimes_f\,(a + b) = a + b \neq\, a\, \oplus_f\,b$ or that the distributive law fails when f-multiplied by the identity. I looked at that other thread too, very interesting. I had of hunch bo's proof but it's nice to see it proved. but furthermore, this gives some very strange laws for multiplication: $v \,\otimes_f\,(k\cdot a) = v\,\otimes_f\,k\,\otimes_f\,a = k\,\otimes_f\,(v \cdot a)$ which means for exponentiation: $v \,\otimes_f\,(a^k) = v \, \otimes_f\,(a^{k-1})\,\otimes_f\,a$ which means f-multiplying a number to the power of another number we convert exponentiation to f-exponentiation: $v \,\otimes_f\,(a^k) = v\,\otimes_f\,(a^{\otimes_f\,k})$ which again is very very inconsistent. I must be doing something incorrect. I think we cannot give the distribution law, but that's not enough for me. I'd really like to know why. I'm absolutely puzzled. « Next Oldest | Next Newest »

 Messages In This Thread help with a distributivity law - by JmsNxn - 09/18/2011, 03:23 PM RE: help with a distributivity law - by tommy1729 - 09/21/2011, 01:51 PM RE: help with a distributivity law - by tommy1729 - 09/21/2011, 06:48 PM RE: help with a distributivity law - by JmsNxn - 09/22/2011, 03:32 PM

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