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 Height of Zero Tetration Problem bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 06/28/2010, 03:26 AM (This post was last modified: 06/28/2010, 03:46 AM by bo198214.) (06/27/2010, 09:50 PM)moejoe Wrote: BUT, taking my 2nd example for why a^0=1 in exponentiation - this doesn't work at all with tetration because if you do the following: "a^^k = y" and "a = y^^(1/k)" ... So to me this all seems like some kind of paradox is happening but I hope that someone will be able to put this in a clear light. I think your paradox emerges from the wrong assumption in your equations. You dont get the inverse of f(x)=x^^k (i.e. the tetration root) by taking x^^(1/k). This is the case for powers but not for tetration. It works for x^k because we have $x^{m\cdot n} = (x^m)^n$ for integer numbers. If we extend this law to rational numbers we can set $x=x^{\frac{1}{n} n} = (x^{\frac{1}{n}})^n$ which means that $x^{\frac{1}{n}$ is the inverse of $x^n$, i.e. $y=x^{\frac{1}{n}}$ is the number such that $y^n = x$. All this consideration fails for tetration because we dont have the rule x^^(m*n)=(x^^m)^^n. « Next Oldest | Next Newest »

 Messages In This Thread Height of Zero Tetration Problem - by moejoe - 06/27/2010, 09:50 PM Tetration root vs x^^(1/k) - by bo198214 - 06/28/2010, 03:26 AM RE: Tetration root vs x^^(1/k) - by bo198214 - 06/28/2010, 06:24 AM RE: Height of Zero Tetration Problem - by moejoe - 06/28/2010, 11:34 PM RE: Height of Zero Tetration Problem - by bo198214 - 06/29/2010, 03:44 AM

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