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

Measuring recovery in deaf, hard-of-hearing, and tinnitus patients in a mental health care setting:validation of the I.ROC

This study was aimed at validating the Individual Recovery Outcomes Counter (I.ROC) for deaf, hard-of-hearing, and tinnitus patients in a mental health care setting. There is a need for an accessible instrument to monitor treatment effects in this population. The I.ROC measures recovery, seeing recovery as a process of experiencing a meaningful life, despite the limitations caused by illness or disability. A total of 84 adults referred to 2 specialist mental health centers for deaf, hard-of-hearing, and tinnitus adults in the Netherlands completed the Dutch version of I.ROC and 3 other instruments. A total of 25 patients refused or did not complete the instruments: 50% of patients using sign language and 18% of patients using spoken language. Participants completed the measures at intake and then every 3 months. In this sample I.ROC demonstrated good internal consistency and convergent validity. Sensitivity to change was good, especially over a period of 6 or 9 months. This study provides preliminary evidence that the I.ROC is a valid instrument measuring recovery for hard-of-hearing and tinnitus patients using spoken language. For deaf patients using sign language, specifically those with limited language skills in spoken and written Dutch, more research is needed.</p

Divorce Reform—One State’s Solution

Although New York has long been a leader in reform legislation, it has also had one of the most ineffective divorce laws in the nation. Therefore, it was not unrealistic to hope that when New York recently revised its divorce laws the new product would serve as a model for future reforms in other jurisdictions. While the new law as finally enacted is defective in several respects, its provisions reflect an attempt to accommodate the basic reform trends in current divorce law. This comment investigates briefly the evolution of governmental controls of divorce, the American tradition prior to the New York reform, and the implications of the procedures finally adopted by that state

Relative systoles of relative-essential 2-complexes

We prove a systolic inequality for the phi-relative 1-systole of a phi-essential 2-complex, where phi is a homomorphism from the fundamental group of the complex, to a finitely presented group G. Indeed we show that universally for any phi-essential Riemannian 2-complex, and any G, the area of X is bounded below by 1/8 of sys(X,phi)^2. Combining our results with a method of Larry Guth, we obtain new quantitative results for certain 3-manifolds: in particular for Sigma the Poincare homology sphere, we have sys(Sigma)^3 < 24 vol(Sigma).Comment: 20 pages, to appear in Algebraic and Geometric Topolog

Real-Time MRI of Continent and Stress Incontinent Male Patients after Orthotopic Ileal Neobladder

Introduction: The aim of this study was to correlate anatomic differences with continence status in male patients after cystoprostatectomy and ileal neobladder using real-time magnetic resonance imaging. Patients and Methods: Anatomic differences of 14 male patients (7 daytime continent and 7 stress incontinent) with ileal neobladder were determined by measuring the orthogonal distance of the bladder neck to the pubococcygeal line (PCL) to correlate anatomic differences with continence status. Results: The median distance of the bladder neck to PCL was +5.4 mm in continent patients before voiding whereas in incontinent patients it was +2 mm (p = 0.012). During the Valsalva maneuver, the median distance in continent patients was +4 and in incontinent patients -3 mm (p = 0.003). At the end of micturition, the median distance was +2.3 mm in continent patients and -12 mm in incontinent patients (p = 0.002). Conclusions: The bladder neck in incontinent patients showed more pronounced mobility in relation to the PCL during micturition and the Valsalva maneuver as compared to continent patients. In addition, the ileal neobladder was positioned significantly lower in the pelvis of incontinent patients. These preliminary results suggest that a stable bladder neck may be an important factor to reach full continence in patients with ileal neobladder. Copyright (C) 2011 S. Karger AG, Base