[Ezekiel]

Mathematicians can prove, it turns out, that the sets of even numbers, whole numbers, and fractions are all the same size – an infinite number known as ℵ0 (pronounced “aleph-null”). The set of reals, on the other hand – that is, all rational and irrational numbers – is much bigger.

Exactly how much bigger, though, is a question that is already pushing at the limits of what we know and can prove.

This is so not complicated. I learned this particular secret of the universe from a space toy:

"To infinity... and beyond!" ~ Buzz Lightyear

"אל האינסוף... ומ*עבר* לו!"

As long as Hebrew has entered the room, "beyond" is based on עבר, the very root of "Hebrew".

the new cardinals nevertheless spell trouble for some mathematicians’ pictures of infinity. The problem lies in a property called Hereditary Ordinal Definability, or “HOD” – the idea that a set, even an infinitely large one, can be understood by sort of “counting up to” it.

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Hod (Hebrew הוֹד Hōḏ, lit. 'majesty, splendour, glory')[1][2] is the eighth sephira of the Kabbalistic Tree of Life. It is positioned on the left side of the tree beneath Gevurah (severity) and directly opposite Netzach (eternity).

Hod is associated with qualities such as submission, humility, and intellectual rigor. It represents the capacity to comprehend and articulate divine truths, balancing the emotive and instinctual energies of Netzach. This balance is crucial for maintaining the flow of divine energy through the sefirot and manifesting it in the material world. Hod is also linked to the planet Mercury and the archangel Michael in Western esoteric traditions.

Hod

<<<

Hod... is the eighth sephira:

∞

"Help, I've fallen and I can't get up!"

large cardinals

I can understand why this article is fixated. Tis the Season!

[BipolarBob]

https://www.youtube.com/watch?v=-PKpxebwbe0

[The Spirit Of Allegiance]

Hypothesis: those who study negative infinities, account for little.

I'll give this article an Absolute Value of +1 as written.

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FROM THE ARTICLE:
We’re into the world of large cardinals Continuing Resolutions now: numbers "so large that one cannot prove they exist using the standard axioms of mathematics...If exacting and ultraexacting cardinals are accepted...ultimately, chaos, not order, wins out....

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It's time to duck-call out those quacks who calculatedly sine unrepentant and cardinally, those who feather their nests doing endless egg-quations as the eggheads they are. They're robin us blind.

Hat tip to Ezekiel for the ordinal and highly insubordinate ping to this thread.

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It's time to...

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[Pete from Shawnee Mission]

John Donne, Anglican Cleric on a specialized infinite set.

"From round earths four imagined corners blow, Your trumpets Angels and arise, arise you numberless infinities of souls And to your scattered bodies go!"

Numberless infinities of souls....The "Theta" set.

("Numberless infinities"...ponder that for a bit.)