Why does 1**2**3**4**5 raise a MemoryError?

[Steven D'Aprano]

On Mon, 01 Apr 2013 00:39:56 +0000, Alex wrote:

> Chris Angelico wrote:
> 
> 
>> Opening paragraph, "... exponentiation, which groups from right to
>> left". It follows the obvious expectation from mathematics. (The OP is
>> using Python 2, but the same applies.)
> 
> Thanks. I did miss that parenthetical comment in para 6.15, and that
> would have been the correct place to look, since it appears that
> operators are not parts of expressions, but rather separate them. Is
> that the "obvious expectation from mathematics," though? Given that
> 
>   3
>  5
> 4
> 
> (i.e.: 4**5**3) is transitive, I would have expected Python to exhibit
> more consistency with the other operators. I guess that is one of the
> foolish consistencies that comprise the hobgoblins of my little mind,
> though.

I don't think you mean "transitive" here. Transitivity refers to 
relations, not arbitrary operators. If ≎ is some relation, then it is 
transitive if and only if:

x ≎ y and y ≎ z implies that x ≎ y.

http://en.wikipedia.org/wiki/Transitive_relation

Concrete examples of transitive relations: greater than, equal to, less 
than and equal to.

On the other hand, "unequal to" is not a transitive relation. Nor is 
"approximately equal to". Suppose we say that two values are 
approximately equal if their difference is less than 0.5:

2.1 ≈ 2.4 and 2.4 ≈ 2.7
but 2.1 ≉ 2.7


Exponentiation is not commutative:

2**3 != 3**2

nor is it associative:

2**(3**2) != (2**3)**2


so I'm not really sure what you are trying to say here.



-- 
Steven