something about a transfinite extension of the fair share sequence? maybe a reasonable answer to what the ωth term is?
November 3, 2026 at 1:56 AM
something about a transfinite extension of the fair share sequence? maybe a reasonable answer to what the ωth term is?
u could use transfinite ordinals to sensibly describe the notion of "infinite zeros then a 1" but decimal notation does not assign any meaning to digits that come after you run out of natural-number-indexed digits
November 1, 2026 at 4:52 AM
u could use transfinite ordinals to sensibly describe the notion of "infinite zeros then a 1" but decimal notation does not assign any meaning to digits that come after you run out of natural-number-indexed digits
I guess the recursive generation rule extends naturally to the transfinite. Namely, w_{alpha+1} should be (w_alpha)(\bar w_alpha), combining the previous sequence with its dual, and at limits, just take the accumulating sequence that has been generated. Nice idea!
November 3, 2026 at 2:20 AM
I guess the recursive generation rule extends naturally to the transfinite. Namely, w_{alpha+1} should be (w_alpha)(\bar w_alpha), combining the previous sequence with its dual, and at limits, just take the accumulating sequence that has been generated. Nice idea!
My youngest loves to ask our Google home for videos about bigger than infinity so we been listening to a lot about:
www.rudyrucker.com/infinityandt...
"FROM OMEGA TO EPSILON-ZERO
The #transfinite ordinal numbers can be thought of as arising through counting."
Led me to look up #TransfiniteAutomota
www.rudyrucker.com/infinityandt...
"FROM OMEGA TO EPSILON-ZERO
The #transfinite ordinal numbers can be thought of as arising through counting."
Led me to look up #TransfiniteAutomota
Infinity and the Mind
www.rudyrucker.com
November 1, 2026 at 11:03 PM
My youngest loves to ask our Google home for videos about bigger than infinity so we been listening to a lot about:
www.rudyrucker.com/infinityandt...
"FROM OMEGA TO EPSILON-ZERO
The #transfinite ordinal numbers can be thought of as arising through counting."
Led me to look up #TransfiniteAutomota
www.rudyrucker.com/infinityandt...
"FROM OMEGA TO EPSILON-ZERO
The #transfinite ordinal numbers can be thought of as arising through counting."
Led me to look up #TransfiniteAutomota
Transfinite induction? Well I’m TRANSgender!!!!
October 28, 2026 at 3:52 PM
Transfinite induction? Well I’m TRANSgender!!!!
It is often the case that proofs using Zorn's lemma can be made more explicit using transfinite recursion (in a smarter way than just unfolding the proof of Zorn's lemma). Is there such a thing for Alexander's subbase theorem? I'm finding it hard to get an intuition for than the standard proof […]
Original post on mathstodon.xyz
mathstodon.xyz
October 28, 2026 at 2:59 PM
It is often the case that proofs using Zorn's lemma can be made more explicit using transfinite recursion (in a smarter way than just unfolding the proof of Zorn's lemma). Is there such a thing for Alexander's subbase theorem? I'm finding it hard to get an intuition for than the standard proof […]
Megabyte was an impressive evil, but I always liked Hexadecimal better.
Transfinite power, the shifting masks, the complete disregard for reality - yet in the end, when push came to shove, she was capable of love and friendship. She transcended what a virus is expected to be.
Transfinite power, the shifting masks, the complete disregard for reality - yet in the end, when push came to shove, she was capable of love and friendship. She transcended what a virus is expected to be.
October 21, 2026 at 1:13 PM
Megabyte was an impressive evil, but I always liked Hexadecimal better.
Transfinite power, the shifting masks, the complete disregard for reality - yet in the end, when push came to shove, she was capable of love and friendship. She transcended what a virus is expected to be.
Transfinite power, the shifting masks, the complete disregard for reality - yet in the end, when push came to shove, she was capable of love and friendship. She transcended what a virus is expected to be.
Just the concept 'transfinite power' enthralled me at first. Knowing Megabyte envied that, but could never have it because they were polar opposites, order versus chaos, was intriguing.
Then finding out they were 'siblings', Hex's injury destabilizing her, Megabyte enslaving her for a time...
Then finding out they were 'siblings', Hex's injury destabilizing her, Megabyte enslaving her for a time...
October 21, 2026 at 2:16 PM
Just the concept 'transfinite power' enthralled me at first. Knowing Megabyte envied that, but could never have it because they were polar opposites, order versus chaos, was intriguing.
Then finding out they were 'siblings', Hex's injury destabilizing her, Megabyte enslaving her for a time...
Then finding out they were 'siblings', Hex's injury destabilizing her, Megabyte enslaving her for a time...
You know how much those eyebrow pencils cost me out of pocket? Sephora ain’t cheap. Had to forgo rulers for the classroom so all the trans girls can do their brows while learning about transfinite numbers.
October 20, 2026 at 5:16 PM
You know how much those eyebrow pencils cost me out of pocket? Sephora ain’t cheap. Had to forgo rulers for the classroom so all the trans girls can do their brows while learning about transfinite numbers.
Theorem 2.14 (Transfinite Induction): Let C be a class of ordinals and assume:
(i) 0 in C
(ii) if alpha in C, then alpha + 1 in C
(iii) if alpha is a nonzero limit ordinal and beta in C for all beta < alpha, then alpha in C.
Then C is the class of all ordinals. (more)
(i) 0 in C
(ii) if alpha in C, then alpha + 1 in C
(iii) if alpha is a nonzero limit ordinal and beta in C for all beta < alpha, then alpha in C.
Then C is the class of all ordinals. (more)
October 20, 2026 at 10:08 PM
Theorem 2.14 (Transfinite Induction): Let C be a class of ordinals and assume:
(i) 0 in C
(ii) if alpha in C, then alpha + 1 in C
(iii) if alpha is a nonzero limit ordinal and beta in C for all beta < alpha, then alpha in C.
Then C is the class of all ordinals. (more)
(i) 0 in C
(ii) if alpha in C, then alpha + 1 in C
(iii) if alpha is a nonzero limit ordinal and beta in C for all beta < alpha, then alpha in C.
Then C is the class of all ordinals. (more)
I want to say my size but It can't be described only by crushing fast-growing hierarchies ,make infinitesimal transfinite numbers , using pseudo-real and surreal Conway and Knuth numbers ordinal order to explain how I'm much bigger , exploring beyond the cardinality of the continuum... Oops ~
October 13, 2026 at 5:27 PM
I want to say my size but It can't be described only by crushing fast-growing hierarchies ,make infinitesimal transfinite numbers , using pseudo-real and surreal Conway and Knuth numbers ordinal order to explain how I'm much bigger , exploring beyond the cardinality of the continuum... Oops ~
Near horizon boundary conditions of black holes feel conceptually similar to the notion of what's 'between' this moment & the next.
Meaning the delta (or whatever's driving the delta) between time 1 & time 2
Thinking about them as an analogy for transfinite automata
www.youtube.com/watch?v=Qw2i...
Meaning the delta (or whatever's driving the delta) between time 1 & time 2
Thinking about them as an analogy for transfinite automata
www.youtube.com/watch?v=Qw2i...
Daniel Grumiller - Interacting black holes and near horizon symmetries - Talk
YouTube video by iiptv
www.youtube.com
October 14, 2026 at 6:05 PM
Near horizon boundary conditions of black holes feel conceptually similar to the notion of what's 'between' this moment & the next.
Meaning the delta (or whatever's driving the delta) between time 1 & time 2
Thinking about them as an analogy for transfinite automata
www.youtube.com/watch?v=Qw2i...
Meaning the delta (or whatever's driving the delta) between time 1 & time 2
Thinking about them as an analogy for transfinite automata
www.youtube.com/watch?v=Qw2i...
"Through I don't know what Mobius effect, representation itself has also turned in on itself, and the whole logical universe of the political is dissolved at the same time, ceding its place to a transfinite universe of simulation, where from the beginning no one is rep..."
- Simulacra and Simulation
- Simulacra and Simulation
October 13, 2026 at 11:55 PM
"Through I don't know what Mobius effect, representation itself has also turned in on itself, and the whole logical universe of the political is dissolved at the same time, ceding its place to a transfinite universe of simulation, where from the beginning no one is rep..."
- Simulacra and Simulation
- Simulacra and Simulation
Today's Reboot remaster episode includes the phrase "transfinite" which is great
October 2, 2026 at 4:58 PM
Today's Reboot remaster episode includes the phrase "transfinite" which is great
Makes you wonder why they haven't started shipping consoles with transfinite numbers yet. But once you hit aleph0, where do you go for the next hardware generation? You'd have to jump straight to the continuum hypothesis just to price the Pro model.
October 3, 2026 at 9:38 AM
Makes you wonder why they haven't started shipping consoles with transfinite numbers yet. But once you hit aleph0, where do you go for the next hardware generation? You'd have to jump straight to the continuum hypothesis just to price the Pro model.
Forget super intelligence, we're doing transfinite intelligence
October 2, 2026 at 9:06 AM
Forget super intelligence, we're doing transfinite intelligence
My piece was about this concept:
Transfinite number | Cantor’s theory, cardinality, infinity | Britannica
Transfinite number, denotation of the size of an infinite collection of objects. Comparison of certain infinite collections suggests that they have different sizes even though they are all infinite. F...
www.britannica.com
September 30, 2026 at 10:20 AM
My piece was about this concept:
Abraham Rueda Zoca: Transfinite octahedrality in spaces of operators https://arxiv.org/abs/2609.24414 https://arxiv.org/pdf/2609.24414 https://arxiv.org/html/2609.24414
September 22, 2026 at 6:48 AM
Abraham Rueda Zoca: Transfinite octahedrality in spaces of operators https://arxiv.org/abs/2609.24414 https://arxiv.org/pdf/2609.24414 https://arxiv.org/html/2609.24414
infinite women? are they transfinite, like ℵ₀?
I will find a way to fumble this. Just you watch.
September 21, 2026 at 3:04 AM
infinite women? are they transfinite, like ℵ₀?
"Mellin Transforms, Transfinite Diameter and Rational Approximations of Integrals" by Francis Brown. #ExperimentalMath #MathSky #NumberTheory
www.tandfonline.com/doi/full/10....
www.tandfonline.com/doi/full/10....
Mellin Transforms, Transfinite Diameter and Rational Approximations of Integrals
We establish a higher-dimensional irrationality criterion for periods which are presented as Mellin integrals depending on many parameters. The criterion is stated as an upper bound on the multi-variate transfinite diameter of the image of the domain of integration under the Mellin arguments. Most of the paper is devoted to studying notions of transfinite diameter relative to very general multivariate Vandermonde matrices. As a proof of principle, we illustrate how this approach works with detailed computations in the case of a 5-parameter family of integrals for \zeta(2) on \mathcal{M}_{0,5}, the moduli space of curves of genus 0 with 5 marked points. This yields a “higher-dimensional” proof of the irrationality of \zeta(2), based on an upper bound for a certain kind of transfinite diameter associated to \mathcal{M}_{0,5}.
www.tandfonline.com
September 21, 2026 at 8:27 AM
"Mellin Transforms, Transfinite Diameter and Rational Approximations of Integrals" by Francis Brown. #ExperimentalMath #MathSky #NumberTheory
www.tandfonline.com/doi/full/10....
www.tandfonline.com/doi/full/10....
When AI superintelligence engages in a conversation with itself in abstraction and then makes an autonomous decision, does it do so rectilinearly (create a new transfinite set of conditions) like the human brain?
I asked AI and it said no. That's a limitation of AI's capacity.
I asked AI and it said no. That's a limitation of AI's capacity.
September 21, 2026 at 3:38 AM
When AI superintelligence engages in a conversation with itself in abstraction and then makes an autonomous decision, does it do so rectilinearly (create a new transfinite set of conditions) like the human brain?
I asked AI and it said no. That's a limitation of AI's capacity.
I asked AI and it said no. That's a limitation of AI's capacity.
When AI superintelligence engages in a conversation with itself in abstraction and then makes an autonomous decision, does it do so rectilinearly (create a new transfinite set of conditions) like the human brain?
I asked AI and it said no. That's a limitation of AI's capacity.
I asked AI and it said no. That's a limitation of AI's capacity.
September 20, 2026 at 2:58 AM
When AI superintelligence engages in a conversation with itself in abstraction and then makes an autonomous decision, does it do so rectilinearly (create a new transfinite set of conditions) like the human brain?
I asked AI and it said no. That's a limitation of AI's capacity.
I asked AI and it said no. That's a limitation of AI's capacity.
When AI superintelligence engages in a conversation with itself in abstraction and then makes an autonomous decision, does it do so rectilinearly (create a new transfinite set of conditions) like the human brain?
I asked AI and it said no. That's a limitation of AI's capacity.
I asked AI and it said no. That's a limitation of AI's capacity.
September 20, 2026 at 2:29 AM
When AI superintelligence engages in a conversation with itself in abstraction and then makes an autonomous decision, does it do so rectilinearly (create a new transfinite set of conditions) like the human brain?
I asked AI and it said no. That's a limitation of AI's capacity.
I asked AI and it said no. That's a limitation of AI's capacity.
Yes. I think the best statement of the intuition “maybe it’s more complicated than that” is actually this 2008 sci fi story about a magic flash drive.
Jack and the Aktuals, or, Physical Applications of Transfinite Set Theory - Reactor
Like many other stories and novels by Rudy Rucker, "Jack and the Aktuals" is a wild and wooly dramatization of certain principles of higher mathematics, with added talking animals, sentient pencils, and orders-of-infinity nested within one another like Russian dolls. No description can ever encompass the mind-bending experience of reading a Rudy Rucker story.
reactormag.com
September 20, 2026 at 4:14 AM
Yes. I think the best statement of the intuition “maybe it’s more complicated than that” is actually this 2008 sci fi story about a magic flash drive.