Infinity problem

[Philosophy Explorer]

Suppose we have x to the x to the x to the x (ad infinitum)
= 2. Then what does x equal?

PhilX

[Dalek Prime]

http://www.had2know.com/academics/power ... ation.html

[Philosophy Explorer]

http://www.had2know.com/academics/power ... ation.html

Interesting. Do you have an answer to the problem I posed? There is a method that will easily let you solve it.

PhilX

[Dalek Prime]

No, but it's a set, isn't it? I'm terrible at math. Hence I, paradoxically, program.

Honestly, I don't know. Don't think I've considered infinite tetration and convergence before.

[Philosophy Explorer]

No, but it's a set, isn't it? I'm terrible at math. Hence I, paradoxically, program.

Honestly, I don't know.

I will let it run for another week before I give the method with the answer to let others have a chance to solve this problem.

Would you like to discuss some easy concepts in number theory?

PhilX

[Dalek Prime]

I think I'm ill-equiped to to give you value, and would not wish to take up your time. But thank you.

I wasn't even able to divide 1 by 1.414 in my head, though the answer made me smack it lol!

[Philosophy Explorer]

I think I'm ill-equiped to to give you value, and would not wish to take up your time. But thank you.

I wasn't even able to divide 1 by 1.414 in my head, though the answer made me smack it lol!

I'll post the method here. The square root of 2 is equal to 1.414, right? Now multiply numerator and denominator of 1 divided by sq rt 2 to get sq rt 2 divided by 2. Substitute 1.414 for the sq rt 2 to get 1.414/2 = .707 which is your answer. Simple? (but a bit wordy)

Do you have links to websites showing graphs of tower powers? Would like to see what they look like.

PhilX

Edit: Just found this (the image in the upper left-hand corner is the one that relates):

https://www.google.com/search?q=power+t ... d=0CCYQ7Ak

PhilX

[Dalek Prime]

Isn't there a graph on my posted link?

Sorry, there isn't a graph there. I'll look.

Update: couldn't find any decent ones, but try this PDF on the topic. Maybe it's of value to you.

http://skysrv.pha.jhu.edu/~neyrinck/extessay.pdf

[Arising_uk]

I'll post the method here. The square root of 2 is equal to 1.414, right? ...

But it isn't?

[Philosophy Explorer]

I'll post the method here. The square root of 2 is equal to 1.414, right? ...

But it isn't?

To the third decimal point, it is.

PhilX

[Arising_uk]

Since when does 1.999396 = 2?

[Philosophy Explorer]

Since when does 1.999396 = 2?

Which hat did you pick that from?

PhilX

[Arising_uk]

Which hat did you pick that from? PhilX

I multiplied 1.414 by itself? I thought a square root was the number obtained by multiplying a number by itself? Can't seem to get 2 from your number?

[Philosophy Explorer]

Which hat did you pick that from? PhilX

I multiplied 1.414 by itself? I thought a square root was the number obtained by multiplying a number by itself? Can't seem to get 2 from your number?

Round it off.

PhilX

[Arising_uk]

1.9994?