# x^x, x^(x^x), x^(x^(x^x)) and so on… [closed]

Is there a general name for functions such as these? Can anyone tell me where to find more information on such functions, or any other connections in math, especially concerning the maximums and minimums of their plots?

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I voted to close as off-topic. But see for example: en.wikipedia.org/wiki/Knuth%27s_up-arrow_notation –  Ryan Budney Jun 11 '11 at 7:37
Do you really mean the bracketing to be as in the title? That is, are you looking at the functions $x^{x^n}$? My guess is that you intend them the other way: x^(x^(x^x)) etc. –  gowers Jun 11 '11 at 7:50
–  Harun Šiljak Jun 11 '11 at 8:24
If gowers is right then there are some relevant plots here: mathdl.maa.org/images/upload_library/22/Ford/Knoebwl235-252.pdf –  solbap Jun 11 '11 at 8:35
I don't disagree with the closure of the question, and some of the latter comments somehow say what I want to say, still it might be worth stressing it as it contradicts some earlier comments: using parenthesis avoids confusion, but still I'd maintain that there is a convention for x^x^x which of course is x^(x^x) and not (x^x)^x. And, to suggest precisely the value 2, to make a point for the (supposed) need for parenthesis seems a bit odd to me (whatever the motivation). Also, perhaps the intention was actually to ask for the limit of the implicitly defined sequence (where it exists). –  quid Jun 11 '11 at 11:10
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## closed as off topic by algori, Ryan Budney, Daniel Litt, Qiaochu Yuan, Dan PetersenJun 11 '11 at 8:36

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