首页 | 本学科首页   官方微博 | 高级检索  
     


Why Numbers Are Sets
Authors:Eric Steinhart
Affiliation:(1) Department of Philosophy, William Paterson University, 300 Pompton Road 265 Atrium Bldg, Wayne, NJ, 07470-2152, U.S.A
Abstract:I follow standard mathematical practice and theory to argue that the natural numbers are the finite von Neumann ordinals. I present the reasons standardly given for identifying the natural numbers with the finite von Neumann's (e.g., recursiveness; well-ordering principles; continuity at transfinite limits; minimality; and identification of n with the set of all numbers less than n). I give a detailed mathematical demonstration that 0 is { } and for every natural number n, n is the set of all natural numbers less than n. Natural numbers are sets. They are the finite von Neumann ordinals.
Keywords:
本文献已被 SpringerLink 等数据库收录!
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号