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- what's the acc for?: lifestreaming
- mainly tweet: my thoughts
- twitter stance: anything is OK
- what kind of ppl do u want to connect with?: ppl who share my hobbies
- free space:
5th grade~ unschooler / lives alone in late grandma's house / receives $700 a month from parents

yuuki ゆうき(金野裕希)<p>wanted an ai pfp but no different than me irl</p><p>cr: <a href="https://www.pixiv.net/artworks/110547305" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://www.</span><span class="">pixiv.net/artworks/110547305</span><span class="invisible"></span></a></p>
yuuki ゆうき(金野裕希)<p>started using my jpn acc.<br />i quote n translate some tweets on this acc smtm.<br />maybe once a month.<br />@yuuki170<br /><a href="https://x.com/i/user/1672629051419410435" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">x.com/i/user/16726290514194104</span><span class="invisible">35</span></a></p>
yuuki ゆうき(金野裕希)<p>i decided to put my blog&#39;s source on Gist.<br />still under maintenance.<br /><a href="https://gist.github.com/yuuki15/6f4dd4a6ce7f5b23cd06f86394d17269" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">gist.github.com/yuuki15/6f4dd4</span><span class="invisible">a6ce7f5b23cd06f86394d17269</span></a></p>
yuuki ゆうき(金野裕希)<p>I&#39;ve uploaded some of my videos etc to archive.org.<br />hope they will remain until a future where youtube is gone.<br /><a href="https://archive.org/search?query=creator%3A%22yuuki+%E3%82%86%E3%81%86%E3%81%8D%28%E9%87%91%E9%87%8E%E8%A3%95%E5%B8%8C%29%22" target="_blank" rel="nofollow noopener noreferrer" translate="no"><span class="invisible">https://</span><span class="ellipsis">archive.org/search?query=creat</span><span class="invisible">or%3A%22yuuki+%E3%82%86%E3%81%86%E3%81%8D%28%E9%87%91%E9%87%8E%E8%A3%95%E5%B8%8C%29%22</span></a></p>
yuuki ゆうき(金野裕希)<p>¹ this indicates &quot;direct implications or relative consistency implications&quot;, tho.<br />(e.g., huge &lt; supercompact)</p><p>in order of both size and strength:<br />• inaccessible &lt; measurable &lt; huge &lt; rank-into-rank &lt; 0=1</p>
yuuki ゆうき(金野裕希)<p>in the large picture,<br />• the size of a number<br />is proportional to<br />• how many numbers it can prove to be consistent.</p><p>the largest number proves the consistency of all numbers, including itself.<br />by Gödel&#39;s theorem, it is a &quot;contradiction&quot;.</p>
yuuki ゆうき(金野裕希)<p>let us write Fin + Inf as ZFC.</p><p>similarly, if we add &quot;a large cardinal exists&quot;, then we can prove the consistency of ZFC.<br />• ZFC + LC ⊢ Con(ZFC)</p>
yuuki ゆうき(金野裕希)<p>by Gödel&#39;s second incompleteness theorem, the axioms &quot;finite numbers exist&quot; can&#39;t prove their own consistency.<br />• Fin ⊬ Con(Fin)</p><p>now if we add &quot;ℵ₀ exists&quot;, then we can prove the consistency of finite numbers.<br />• Fin + Inf ⊢ Con(Fin)</p><p>this shows Fin + Inf &gt; Fin.</p>
yuuki ゆうき(金野裕希)<p>so the Q is, what tf is the largest infinite number.<br />n it&#39;s a &quot;contradiction&quot; (aka 0=1).<br />as drawn in this pic.¹</p><p>let me explain from scratch.</p>
yuuki ゆうき(金野裕希)<p>actually, large cardinals refer to large ♾ with specific properties.</p><p>(the successor of an inaccessible cardinal is not inaccessible by definition.)</p>
yuuki ゆうき(金野裕希)<p>¹ it is shown<br />• ℶ₁ ≠ ℵ₀ (Cantor)<br />• ℶ₁ ≠ ℵ_ω etc. (König&#39;s theorem)<br />tho.</p>
yuuki ゆうき(金野裕希)<p>infinities are written<br />• ℵ₀, ℵ₁, ℵ₂, …, ℵ_ω, …<br />in order from smallest to largest.</p><p>for the number of reals ℶ₁,<br />• ℶ₁ = ℵ_?<br />is not provable from the standard axioms of mathematics.¹</p><p>the ℶ₁ = ℵ₁ conjecture is called the<br />• continuum hypothesis (CH).</p>
yuuki ゆうき(金野裕希)<p>actually, there&#39;s infinitely many infinite numbers.</p>
yuuki ゆうき(金野裕希)<p>¹ already known to the Jains of India (400 BC), tho.<br />but they made mistakes such as the number of points on a line |ℝ| and a plane |ℝ²| are not equal. (both are 2^ℵ₀.)</p>