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It doesn't say that. What it says is:

    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
    instance.
That's not the same thing at all.



I miss quoted the original blog by replacing "has" for "can" and such. But the second sentence of what you quoted is misleading because that's not an correct interpretation of FTA.


    > But the second sentence of what you
    > quoted is misleading because that's
    > not an correct interpretation of FTA.
I wonder if this is a language thing. The second sentence says:

    ... we count the factorizations 3x5x13
    and 13x3x5 as the same, for instance.
This is giving an simple example of what the phrase "up to ordering" implies. The full statement of the FTA says that the factorisation is unique "up to ordering" and that's exactly what the second sentence is saying.

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.


You also misquoted "appropriately" as "approximately", making the meaning completely different.




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