Please improve these comprehensions (was meaning of [ ])

[Marko Rauhamaa]

Ben Finney <ben+python at benfinney.id.au>:
> ram at zedat.fu-berlin.de (Stefan Ram) writes:
>
>>   In mathematics, every author is free to give his own definitions to
>>   concepts and create his own notation.
>
> [...]
>
> For established terms in the field, an author has freedom to redefine
> those terms only to the extent that the author discards clear
> communication with those who already use the established meanings.

In mathematics, it is quite common to define even established terms.
First, that's done because slight terminology variants are in use so
definitions are necessary for clear communication. Secondly, commonly
used symbols are taken into new uses. For example, Boolean algebra
"hijacks" + so that 1 + 1 = 1.

Which reminds me of this puzzle I saw a couple of days ago:

   1 + 4 = 5
   2 + 5 = 12
   3 + 6 = 21
   8 + 11 = ?

A mathematician immediately comes up with a "wrong" answer.


Marko