The fundamental theorem of arithmetic states that
every positive integer can be factorized in one
way as a product of prime numbers. This statement
has to be appropriately interpreted: we count the
factorizations 3x5x13 and 13x3x5 as the same, for
> But the second sentence of what you
> quoted is misleading because that's
> not an correct interpretation of FTA.
... we count the factorizations 3x5x13
and 13x3x5 as the same, for instance.
So I still think you are mistaken, and I don't understand why you are disagreeing with what Gowers wrote. Perhaps you could give more detail about why you think he is wrong.