Should tetration be a multivalued function?

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Should tetration be a multivalued function?

sheldonison $Offline$
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#11

01/09/2016, 06:20 AM

(01/08/2016, 06:26 PM)marraco Wrote: .... No proof, but numerically:
$\vspace{15}{(^{r+1}a)^{^{-(r+1)}a}=(^{-r}a)^{^{r}a}}$

ok, first lets define y and z as follows:
$y=\; ^{-(r+1)}a \;\;\;$
$z=\; ^{r}a \;\;\;$

Then substitute these values of y and z into the Op's equation above, noting that
$^{(r+1)}a = a^z\;\;\;\; ^{-r}a = a^y$

$(a^z)^{y}=(a^y)^z\;\;\;$ This is the Op's equations with the substitutions
$(a^z)^{y}=(a^y)^z=a^{(y\cdot z)}\;\;\;$ this equation holds for all values of a,y,z

- Sheldon

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Messages In This Thread

Should tetration be a multivalued function? - by marraco - 01/03/2016, 11:24 PM

RE: Should tetration be a multivalued function? - by marraco - 01/03/2016, 11:32 PM

RE: Should tetration be a multivalued function? - by andydude - 01/03/2016, 11:55 PM

RE: Should tetration be a multivalued function? - by andydude - 01/04/2016, 12:01 AM

RE: Should tetration be a multivalued function? - by marraco - 01/04/2016, 12:08 AM

RE: Should tetration be a multivalued function? - by andydude - 01/04/2016, 12:35 AM

RE: Should tetration be a multivalued function? - by marraco - 01/04/2016, 03:57 AM

RE: Should tetration be a multivalued function? - by marraco - 01/08/2016, 06:26 PM

RE: Should tetration be a multivalued function? - by marraco - 01/08/2016, 11:05 PM

RE: Should tetration be a multivalued function? - by sheldonison - 01/09/2016, 06:20 AM

RE: Should tetration be a multivalued function? - by marraco - 01/09/2016, 05:56 PM

RE: Should tetration be a multivalued function? - by marraco - 01/14/2016, 04:24 AM

RE: Should tetration be a multivalued function? - by tommy1729 - 01/10/2016, 03:37 AM

RE: Should tetration be a multivalued function? - by marraco - 01/11/2016, 09:28 PM

RE: Should tetration be a multivalued function? - by andydude - 01/13/2016, 08:24 AM

RE: Should tetration be a multivalued function? - by sheldonison - 01/13/2016, 01:37 PM

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