I have a problem reading a discussion forum post. Namely, in the ASCII text, is 2^3^4 the same as $(2^3)^4$ or $2^{3^4}$?
Powers in ASCII text
5
$\begingroup$
notation
arithmetic
exponentiation
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0Related: http://math.stackexchange.com/questions/534578/xyz-is-it-xyz-or-xyz – 2016-08-11
2 Answers
10
I believe that usually the intended meaning of a^b^c or $a^{b^c}$ is $a^{(b^c)}$.
The reason is that if someone wants to write $(a^b)^c$, he can use the equivalent expression $a^{bc}$ instead.
In particular, this seems to be quite common in cardinal arithmetic - I think no one will doubt what is meant when someone writes $2^{2^{\aleph_0}}$ even when it's not indicated by brackets: $2^{(2^{\aleph_0})}$.
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3I'd say $a^{b^c}$ is unambiguously $a^{(b^c)}$, by convention, but I don't think there is a convention about a^b^c, and I don't think it's safe to make any assumption about the writer's intention. – 2012-05-30
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The reason you have a problem is that the notation is ambiguous. A careful writer will write 2^(3^4) or (2^3)^4, depending on what she means. There is no way of telling what 2^3^4 means, except possibly from context.
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3Is the careful writer female? Nice. – 2012-05-29