06/08/2009, 01:28 AM
(This post was last modified: 06/08/2009, 01:43 AM by Base-Acid Tetration.)
well i can't attend the meeting. (what if one of you guys are internet predators or something
)
you guys can instead create a pdf file summarizing the discussion that was held during the meeting, and i can comment on it on this forum.
this tetration thing isn't going too well, obviously. i;m pretty sure they weren't stuck in a quagmire like this when they developed real exponentiation, or iterated multiplication... multiplication, which exponentiation is based on, is both commutative and associative, leading to all of the nice properties, like distributivity of powers over multiplication and a^(x+y) = a^x*a^y.... I saw one day, that the problem is that is addition is commutative and associative, but exponentiation is not, so no function can consistently map addition of numbers to exponentiatiation of numbers. so \( {}^{x+y} a \ne ({}^x a)^{({}^y a)} \), and \( {}^x (a^b) \ne ({}^x a)^{({}^x b)} \)
)you guys can instead create a pdf file summarizing the discussion that was held during the meeting, and i can comment on it on this forum.
this tetration thing isn't going too well, obviously. i;m pretty sure they weren't stuck in a quagmire like this when they developed real exponentiation, or iterated multiplication... multiplication, which exponentiation is based on, is both commutative and associative, leading to all of the nice properties, like distributivity of powers over multiplication and a^(x+y) = a^x*a^y.... I saw one day, that the problem is that is addition is commutative and associative, but exponentiation is not, so no function can consistently map addition of numbers to exponentiatiation of numbers. so \( {}^{x+y} a \ne ({}^x a)^{({}^y a)} \), and \( {}^x (a^b) \ne ({}^x a)^{({}^x b)} \)