- #1
Hertz
- 180
- 8
A power tower (x^^n) is a variable raised to the power of itself n amount of times.
x^^4 = x^x^x^x
x^^3 = x^x^x
x^^2 = x^x
x^^1 = x
I was wondering if an associative property for power towers exists.
Does x^(x^x) equal the same thing as (x^x)^x? Is x^(x^^n) equal to x^^(n + 1)?
If anybody could prove that the order of the exponents doesn't matter if the exponents are the same, that would be great, but an intuitive reasoning would be great also :)
e-
WHOA! I didn't realize I posted this in the physics forum. If anybody would be able to move it to the general math discussion forum that would be great
x^^4 = x^x^x^x
x^^3 = x^x^x
x^^2 = x^x
x^^1 = x
I was wondering if an associative property for power towers exists.
Does x^(x^x) equal the same thing as (x^x)^x? Is x^(x^^n) equal to x^^(n + 1)?
If anybody could prove that the order of the exponents doesn't matter if the exponents are the same, that would be great, but an intuitive reasoning would be great also :)
e-
WHOA! I didn't realize I posted this in the physics forum. If anybody would be able to move it to the general math discussion forum that would be great
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