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! |
|