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99999...9^9^9^9^9^9^9...9!!9!!9!!9!!9...9↑↑↑↑9↑↑↑↑9↑↑↑↑9∞Depends on what is allowed ig
Small note,
9↑↑↑…↑↑9
Would be
near infinitelymuch much much larger than just repeated hexation of 9(Of course even just 9↑↑↑↑9 is too big to be written in the universe, so all of these numbers are practically a microdose of infinity)
It’s not “near infinitely larger” since there are a finite number of numbers before it and an infinite number after it - it’s nowhere close to “near infinitely larger”
Fair enough
I would say it’s incomprehensibly larger, though, which is what I took your meaning for in the first place.
∞ ↑↑↑↑↑… ↑↑↑∞
If we get to bring infinity into the mix, how about larger infinite number sets? Aleph-omega time.
Infinty is a magnitude, not a number
Also BB(8000) can (proven ) not be represented by ZFC so that might take the cake
infinity is great indeed
∞
Infinity isn’t a number, it’s a concept. Some infinities are bigger than others. For example, there’s an infinite amount of real values between 0 and 1 but there’s an even greater infinite amount of real values between 0 and 2.
May as well go through the proofs:
First, we need to establish that two infinities are equal in cardinality (aka size) if all their elements can be 1:1 mapped to each other.
So, to go from the reals within [0, 1] and [0, 2], we can multiply by 2. This maps every value within [0, 1] to every value within [0, 2], so these are of the same cardinality.
Where things get interesting is the proof that the reals within [0, 1] are of greater cardinality than every integer.
Say we have an arbitrary mapping from every integer to a real within [0, 1]:
0 -> 0.89236… 1 -> 0.47389… 2 -> 0.84776… 3 -> 0.18790… 4 -> 0.90542… ⋮ ⋱This list contains every integer, but it does not contain every real number because we can always come up with a new one by ensuring at least one digit is different in each existing real:
0 -> …8… ≠ 9 1 -> …7… ≠ 8 2 -> …7… ≠ 8 3 -> …9… ≠ 0 4 -> …2… ≠ 3 ⋮ ⋱ 0.98803… is not within the listTherefore, no 1:1 mapping between the integers and reals exists. Because the limiting factor is the amount of integers, the cardinality of the reals is greater than that of the integers.
there’s an infinite amount to real values between 0 and 1 but there’s an even greater infinite amount of real values between 0 and 2.
This isn’t true. Both of those sets have the same cardinality as the real numbers. Measuring infinities can be weird that way.
They are both strictly larger than the rationals, though.
Yes, but in that case it’s the same amount. For every real x in the first interval there is a real y=2x in the second. Also for every real y in the second interval there is a real x=y/2 in the first.
“Infinity” and “number” mean different things in different contexts. In the context of set theory, its perfectly valid to talk about infinite numbers, e.g. https://en.wikipedia.org/wiki/Aleph_number
oo
oh, wrong thread
shush
∞…
∀R { { ∀[ψ], t: R([ψ],t) ↔ ([ψ] = “xi ∈ xj” ∧ t(xi) ∈ t(xj)) ∨ ([ψ] = “xi = xj” ∧ t(xi) = t(xj)) ∨ ([ψ] = “(¬θ)” ∧ ¬R([θ], t)) ∨ ([ψ] = “(θ∧ξ)” ∧ R([θ], t) ∧ R([ξ], t)) ∨ ([ψ] = “∃xi(θ)” ∧ ∃t′: R([θ], t′)) (where t′ is a copy of t with xi changed) } ⇒ R([ϕ],s) }
Ah, good ol’ Rayo’s number. I can fit that in a twitter post!
9!!!!!!!!!!![...]False! Create a new number system, base of whatever the chart will accept, then full post of that. :3
Just use an existing system FFFFFFFFFFFFFFFFFFFFFFFFFF
Why stop at base 16?
ZZZ[…]
Joke’s on you, the FFFFFFFFFFFFFFFFFFF was actually written in base 9!!!.. and F simply happened to be mapped to the last integer
But there’s still soooo much left on the tableeeeeeeeeeee!!!
TREE(3)
TREE(4)
tree(tree(tree(tree(tree(tree(tree(tree(tree(tree(tree(tree(3))))))))))))
BB(tree(3))
I’m unfamiliar, what is BB?
Busy beaver algorithm. https://wiki.bbchallenge.org/wiki/Busy_Beaver_Functions
Starting definition: the largest number of steps (or shifts) that any Turing machine (of a certain size, and starting with a blank tape) takes before halting.
Computerphile does a good treatment on it. https://www.youtube.com/watch?v=CE8UhcyJS0I
Maybe grade 4 I said something rude or dumb and had to stay in while the whole class went on an adventure and I decided to determine the largest number ever and I wrote ‘9’ on my notebook about 50 times and then the book report and I never did learn, what is the largest ever number
replace 3 of the nines at the beginning with “10^”
I’m no mathematician, but surely replacing every three 9s with 10^ would be larger, right?
John Madden! John Madden!AEIOU AEIOU AEIOU
BB(9)
10 in base infinity I guess?
Haha have you found the 8?
Fuck I thought I fixed it
10 (base grahams number)
