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He never used the word "approximately", and I think you are reading the statement(s) incorrectly because of that. Let me be more specific.

The article says:

    The fundamental theorem of arithmetic
    states that every positive integer can
    be factorized in one way as a product
    of prime numbers.
OK, so that is an initial statement to give the general idea of what's going on. There are some details that need now to be added to avoid misunderstanding. In particular, the statement needs to be interpreted carefully. Gowers goes on to say:

    This statement has to be appropriately
    interpreted: ...
That's what I just said above ...

    ... we count the factorizations 3x5x13
    and 13x3x5 as the same, for instance.
So this is an example to set the scene for what is to follow. It points out that in the statement of the FTA we are going to regard to factorisations that differ only in the ordering of the factors as being the same.

Reading your other comments, it appears you are arguing against something that you actually agree with, and I suspect you have mis-read or mis-interpreted what Gowers has written.




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