of 0.999... as a finite, indeterminate string with an infinitely small distance from 1 have "not yet constructed a complete process conception of the infinite decimal". Other students who have a complete process conception of 0.999... may not yet be able to "encapsulate" that process into an "object conception", like the object conception they have of 1, and so they view the process 0.999... and the object 1 as incompatible. Dubinsky et al. also link this mental ability of encapsulation to viewing as a number in its own right and to dealing with the set of natural numbers as a whole. Cultural phenomenon With the rise of the Internet, debates about 0.999... have become commonplace on newsgroups and message boards, including many that nominally have little to do with mathematics. In the newsgroup , arguing over 0.999... is described as a "popular sport", and it is one of the questions answered in its FAQ. The FAQ briefly covers , multiplication by 10, and limits, and it alludes to Cauchy sequences as well. A 2003 edition of the general-interest newspaper column The Straight Dope discusses 0.999... via and limits, saying of misconceptions, A Slate article reports that the concept of 0.999... is "hotly disputed on websites ranging from World of Warcraft message boards to Ayn Rand forums". In the same vein, the question of 0.999... proved such a popular topic in the first seven years of Blizzard Entertainment's Battle.net forums that the company issued a "press release" on April Fools' Day 2004 that it is 1: Two proofs are then offered, based on limits and multiplication by 10. 0.999... features also in mathematical jokes, such as: In alternative number systems Although the real numbers form an extremely useful number system, the decision to interpret the notation "0.999..." as naming a real number is ultimately a convention, and Timothy Gowers argues in Mathematics: A Very Short Introduction that the resulting identity 0.999... = 1 is a convention as well: Infinitesimals Some proofs that 0.999... = 1 rely on the Archimedean property of the real numbers: that there are no nonzero infinitesimals. Specifically, the difference 1 − 0.999... must be smaller than any positive rational number, so it must be an infinitesimal; but since the reals do not contain nonzero infinitesimals, the difference is therefore zero, and therefore the two values are the same. However, there are mathematically coherent ordered algebraic structures, including