This paper discusses how the infinite set of real numbers between 0 and 1 could be represented by a countably infinite tree structure which would avoid Cantor’s diagonalization argument that the set of real numbers i...This paper discusses how the infinite set of real numbers between 0 and 1 could be represented by a countably infinite tree structure which would avoid Cantor’s diagonalization argument that the set of real numbers is not countably infinite. Likewise, countably infinite tree structures could represent all real numbers, and all points in any number of dimensions in multi-dimensional spaces. The objective of this paper is not to overturn previous research based on Cantor’s argument, but to suggest that this situation may be treated as a definitional or axiomatic choice. This paper proposes a “non-Cantorian” branch of cardinality theory, representing all these infinities with countably infinite tree structures. This approach would be consistent with the Continuum Hypothesis.展开更多
AIM： To evaluate surgical outcomes（SOs） and visual outcomes（VOs） in cataract surgery comparing the Centurion？ phacoemulsification system（CPS） with the Infiniti？ phacoemulsification system（IPS）.METHODS： Pro...AIM： To evaluate surgical outcomes（SOs） and visual outcomes（VOs） in cataract surgery comparing the Centurion？ phacoemulsification system（CPS） with the Infiniti？ phacoemulsification system（IPS）.METHODS： Prospective, consecutive study in a singlesite private practice. Totally 412 patients undergoing cataract surgery with either the CPS using the 30-degree balanced？ tip（n=207） or the IPS using the 30-degree Kelman？ tip（n=205）. Intraoperative and postoperative outcomes were documented prospectively up to one month follow-up. Nuclear sclerosis（NS） grade, cumulated dissipated energy（CDE）, preoperative corrected distance visual acuity（CDVA）, and CDVA at one month were recorded. RESULTS： CDE was 13.50% less in the whole CPS compared with the whole IPS subcohort. In eyes with NS grade III or greater, CDE was 28.87% less with CPS（n=70） compared with IPS（n=44）（P=0.010）. Surgical complications were not statistically different between the two subcohorts（P=0.083）, but in the one case of vitreous loss using the CPS, CDVA of 6/4 was achieved at one month. The mean CDVAs（VOs） at one month for NS grade III and above cataracts were-0.17 log MAR（6/4.5） in the CPS and-0.15 log MAR（6/4.5） in the IPS subcohort respectively（P=0.033）.CONCLUSION： CDE is 28.87% less, and VOs are significantly improved, in denser cataracts in the CPS compared with the IPS. The authors recommend the CPS for cases with denser nuclei.展开更多
文摘This paper discusses how the infinite set of real numbers between 0 and 1 could be represented by a countably infinite tree structure which would avoid Cantor’s diagonalization argument that the set of real numbers is not countably infinite. Likewise, countably infinite tree structures could represent all real numbers, and all points in any number of dimensions in multi-dimensional spaces. The objective of this paper is not to overturn previous research based on Cantor’s argument, but to suggest that this situation may be treated as a definitional or axiomatic choice. This paper proposes a “non-Cantorian” branch of cardinality theory, representing all these infinities with countably infinite tree structures. This approach would be consistent with the Continuum Hypothesis.
文摘AIM： To evaluate surgical outcomes（SOs） and visual outcomes（VOs） in cataract surgery comparing the Centurion？ phacoemulsification system（CPS） with the Infiniti？ phacoemulsification system（IPS）.METHODS： Prospective, consecutive study in a singlesite private practice. Totally 412 patients undergoing cataract surgery with either the CPS using the 30-degree balanced？ tip（n=207） or the IPS using the 30-degree Kelman？ tip（n=205）. Intraoperative and postoperative outcomes were documented prospectively up to one month follow-up. Nuclear sclerosis（NS） grade, cumulated dissipated energy（CDE）, preoperative corrected distance visual acuity（CDVA）, and CDVA at one month were recorded. RESULTS： CDE was 13.50% less in the whole CPS compared with the whole IPS subcohort. In eyes with NS grade III or greater, CDE was 28.87% less with CPS（n=70） compared with IPS（n=44）（P=0.010）. Surgical complications were not statistically different between the two subcohorts（P=0.083）, but in the one case of vitreous loss using the CPS, CDVA of 6/4 was achieved at one month. The mean CDVAs（VOs） at one month for NS grade III and above cataracts were-0.17 log MAR（6/4.5） in the CPS and-0.15 log MAR（6/4.5） in the IPS subcohort respectively（P=0.033）.CONCLUSION： CDE is 28.87% less, and VOs are significantly improved, in denser cataracts in the CPS compared with the IPS. The authors recommend the CPS for cases with denser nuclei.
