User contributions for Yto

27 August 2023

• 21:1821:18, 27 August 2023 diff hist +2,368‎ Bashicu matrix system ‎ added a bit of intuition Tag: Visual edit: Switched

11 July 2023

• 20:2520:25, 11 July 2023 diff hist +6‎ m Proving well-orderedness ‎No edit summary
• 20:2020:20, 11 July 2023 diff hist +2,489‎ N Proving well-orderedness ‎ Created page with "Proving that an ordered set is well-ordered can be very challenging. The methods that can be used to do this vary depending on the type of ordered set. There are of course cases when none of this applies, but mainly in the context of pure apeirology, it often does apply. <h1>Proving totality</h1> As one of the two conditions for an order to be a well-order is that it is a total order, proving totality is a significant part of the proof of well-orderedness. In arbitraril..."
• 19:0119:01, 11 July 2023 diff hist +273‎ m Ordinal notation system ‎No edit summary
• 17:4017:40, 11 July 2023 diff hist +33‎ m Ordinal notation system ‎No edit summary
• 06:2606:26, 11 July 2023 diff hist +1,517‎ N Pair sequence system ‎ Created page with "'''Pair sequence system''' ('''PSS''') is an ordinal notation system defined by BashicuHyudora. It is also a sequence system with sequences of pairs of natural numbers, and an expansion system with the base of standard form being \( \{((0,0),(1,1),(2,2),...,(n,n)) : n\in\mathbb{N}\} \) and with the expansion \( S[n] \) defined in the following way: - The parent of a pair \( x \) in \( S \) is the last pair before it with a smaller first element. The ance..."
• 06:1606:16, 11 July 2023 diff hist +1,733‎ N Primitive sequence system ‎ Created page with "'''Primitive sequence system''' ('''PrSS''') is an ordinal notation system defined by BashicuHyudora. It is also a sequence system with sequences of natural numbers, and an expansion system with the base of standard form being \( \{(0,1,2,...,n) : n\in\mathbb{N}\} \) and with the expansion \( S[n] \) defined in the following way: If \( B \) is the subsequence of \( S \) such that the first element of \( B \) is the last element of \( S \) strictly smaller..." current
• 05:4905:49, 11 July 2023 diff hist +436‎ m Expansion system ‎No edit summary current
• 05:2205:22, 11 July 2023 diff hist +56‎ m Bashicu matrix system ‎ tex
• 04:3504:35, 11 July 2023 diff hist +36‎ m Sequence system ‎ tex
• 04:3404:34, 11 July 2023 diff hist +823‎ m Bashicu matrix system ‎ fixing stuff and mentioning values
• 04:0704:07, 11 July 2023 diff hist +985‎ N Expansion system ‎ Created page with "An '''expansion system''' is an ordinal notation system defined in a special way. It is defined through expansion, with standard form constructed from a specified set called the base of the standard form (usually with order type \( \omega \)). More precisely, the definition involves only a set S of well-formed terms, a function \( []: S\times\mathbb{N}\to S \) (where [](x,n) is written as x[n]), and a set \( X_0 \). Then with \( X \) being the closure of \( X_0 \) u..."
• 04:0304:03, 11 July 2023 diff hist +808‎ N Sequence system ‎ Created page with "A '''sequence system''' is an ordinal notation system in which sequences are well-ordered. Typically, it is an expansion system, with the expansion chosen so that x[n] is always lexicographically smaller than x, and additionally, so that x[0] is x without its last element and x[n] is always a subsequence of x[n+1]. If all of these hold, then as long as the base of its standard form is totally ordered, the order of the sequence system is identical to the lexicogr..." Tag: Visual edit: Switched
• 03:2103:21, 11 July 2023 diff hist +49‎ m Cantor normal form ‎ added some links Tag: Visual edit
• 03:1703:17, 11 July 2023 diff hist −7,123‎ User:Yto ‎ Replaced content with "Hi, i've been an apeirologist for approximately 5 years. I recently published a [https://arxiv.org/abs/2307.04606 proof] that BMS is well-founded." current Tag: Replaced
• 02:4802:48, 11 July 2023 diff hist +26‎ m Bashicu matrix system ‎ added source Tag: Visual edit
• 02:4602:46, 11 July 2023 diff hist −12‎ m Bashicu matrix system ‎No edit summary
• 00:1600:16, 11 July 2023 diff hist −42‎ m Bashicu matrix system ‎No edit summary

10 July 2023

• 22:1522:15, 10 July 2023 diff hist −1‎ m Bashicu matrix system ‎No edit summary
• 22:1222:12, 10 July 2023 diff hist −2‎ m Ordinal notation system ‎No edit summary
• 22:1122:11, 10 July 2023 diff hist +920‎ N Ordinal notation system ‎ Created page with "An '''ordinal notation system''' (also called an '''ordinal notation''' informally) is a system of names for ordinals, or equivalently, a well-ordered set of objects that "can be considered names". There may not be a formal restriction of what objects can be considered names, but most common examples include strings, sequences, trees/hydras, and terms built up from constants and functions. Most authors also require the well-order to be recursive, and this requirement is..."
• 22:0022:00, 10 July 2023 diff hist +11‎ m Bashicu matrix system ‎ i managed to miss a subscript
• 22:0022:00, 10 July 2023 diff hist +231‎ m Bashicu matrix system ‎ subscripts are now actually subscripts. hopefully all of them.
• 21:5321:53, 10 July 2023 diff hist +1,970‎ Bashicu matrix system ‎ made the page nontrivial Tag: Visual edit

4 September 2022

• 13:5413:54, 4 September 2022 diff hist +4,264‎ User:Yto ‎No edit summary

3 September 2022

• 23:4023:40, 3 September 2022 diff hist +2,771‎ User:Yto ‎No edit summary
• 22:3622:36, 3 September 2022 diff hist +262‎ N User:Yto ‎ Created page with "Hi, i've been an apeirologist for approximately 4 years. I thought about writing articles on this wiki, but realized that i'm bad at finding sources, so i'll just use this page for unsourced explanations and philosophy related to apeirology. Hopefully that's ok."