When is .999... less than 1?

We examine alternative interpretations of the symbol described as nought, point, nine recurring. Is "an infinite number of 9s" merely a figure of speech? How are such alternative interpretations related to infinite cardinalities? How are they expressed in Lightstone's "semicolon" notation? Is it possible to choose a canonical alternative interpretation? Should unital evaluation of the symbol .999 . . . be inculcated in a pre-limit teaching environment? The problem of the unital evaluation is hereby examined from the pre-R, pre-lim viewpoint of the student.Comment: 28 page

The Philosophy of Midcentury Corporation Statutes

Professor Katz, in a Symposium issue for another journal, theorizes about the purpose of corporation statutes. At its heart, the theory of business enterprise attempts to delineate the areas of risk, control, and profit, that partners can allocate amongst themselves and to define defaults when these areas are not allocated. Statutes are approached three ways: enabling, which gives ample freedom to corporations to structure themselves; mix, which provides a statutory structure but still relies on corporate responsibility; and a paternal responsibility structure, which limits what a corporation can do; and a fourth approach, a social responsibility theory not yet reflected in statutes, that advocates that corporations should include the public good when making decisions. Professor Katz then considers various statutory topics within the framework of the three approaches. Most of the statutes that Professor Katz examines fall into the first theory, enabling statutes; North Carolina statutes are the only that apply the other two theories. Interestingly, the dominant enabling theory is one that has been under attack for almost one hundred years; and the new revolution of statutes (corporate gifts to charity) will not have the impact others think it will, but rather will serve as an impetus to ensure that there is still a means by which to punish corporations