| viXra.org > Set Theory and Logic > viXra:2411.0024 |
 |
 |
| viXra.org > Set Theory and Logic > viXra:2411.0024 |
|
|
Set Theory and Logic |
|
Authors: Amel Mara
The significance of the Inductive Hypothesis is examined with respect to the Principle of Mathematical Induction. A few relevant theorems that involve functions in set theory are specified with respect to the Inductive Hypothesis. The countability of rational numbers is reviewed, as to Cantor’s "intuition" (i.e., the "zig-zag" method of enumerating rational numbers) and constructive formulas that would map the set of natural numbers to a subset of the rational numbers (e.g., a multiplicative inverse function, a divisive function). Von Neumann and Zermelo ordinals are introduced to support the definition of a non-dense, well-ordered set of numbers. It is determined that for a specific infinite set of ordinals with a maximal element that is a limit ordinal, the set must contain at least one successor ordinal that cannot be recursively accessed in a finite number of steps from a specified base ordinal.
Comments: 32 Pages.
Download: PDF
[v1] 2024-11-04 20:17:05
[v2] 2024-11-11 17:14:12
[v3] 2024-12-04 19:20:21
[v4] 2025-01-29 16:36:16
Unique-IP document downloads: 510 times
Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.
Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.
| Third-Party Links: |
|