On Sunday, 22 October 2017 at 14:44:04 UTC, Timon Gehr wrote:
On 22.10.2017 16:20, Ilya Yaroshenko wrote:
.. i thought it should be (2 ^^ 1) ^^ 2 = 4
2 ^^ (1 ^^ 2) == 2
It is standard for ^/**/^^ to be right-associative. (This is
also the standard convention in mathematics.)
Yeah, and a height-3 tower $a^{b^c}$ (TEX notation) actually
means "a to the power of (b to the power of c)", not the other
way around. Otherwise, it can be written as $a^{b \cdot c}$,
which is only a height-2 tower.
The convention also makes at least the following sense. An
expression like
(((a ^^ b) ^^ c) ^^ d) ^^ e
already has an almost bracket-free notation as
a ^^ (b * c * d * e).
So it is useful to have a bracket-free way to write the
other-way-associative variant,
a ^^ (b ^^ (c ^^ (d ^^ e))).
Ivan Kazmenko.
