# Notation for Cartesian power, an oddity in the international standard

The Cartesian product of $A$ with itself $n$ times is normally denoted using superscript notation $A^n$, and this what ISO 31-11 defined as standard. However, ISO 31-11 has been superseded by ISO 80000-2, which specifies the notation as using a subscript: $A_n$, in clause 2.5.7: “$A × A × \ldots × A$ is denoted by $A_n$, where $n$ is the number of factors in the product.”

This looks rather odd and easily confuses with other uses for subscripting. Can this be a typo? I am specifically reading SFS-ISO 80000-2, which contains the subscript notation both in the English text and in the Finnish text. But I have not seen such usage in real life. And BS ISO 80000-2 appears to use a superscript here. What about other national implementations of ISO 80000-2?

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Always link to standards when possible. I agree, if that's what the standard says, it is misguided. –  Thomas Andrews Jun 22 '12 at 13:04
That is the standard for use in the Natural Sciences and Technology. Not for use in mathematics. –  GEdgar Jun 22 '12 at 14:06
Why didn't he link to it? Because it is a "pay" standard: you need to pay a fee to read it! I think. –  GEdgar Jun 22 '12 at 14:08
@Gedgar, yes, it is a “pay” standard, as ISO standards mostly are. Its [description page][iso.org/iso/iso_catalogue/catalogue_tc/… says: “The recommendations in ISO 80000-2:2009 are intended mainly for use in the natural sciences and technology, but also apply to other areas where mathematics is used.” –  Jukka K. Korpela Jun 22 '12 at 14:16