Completed versus Incomplete Infinity in Arithmetic

Completed versus Incomplete Infinity in Arithmetic by Edward Nelson Department of Mathematics, Princeton University The numbers are 0, 1, 2, 3, . . . . The numbers form the simplest infinity, so if we want to understand infinity we should try to understand the numbers. Rather than use the symbols 1, 2, etc. originating in India, let us use the notation of mathematical logic: the numbers are 0, S0, SS0, SSS0, .

• point of view with great simplification of the technical tools
• notation of mathematical logic
• numbers as input
• incomplete infinity
• time function
• time as a function
• computational complexity
• infinity
• mathematics
• 3 mathematics
• numbers