This is interesting: the opposite of "Explicit is better than implicit" is "Convention over configuration"
in other words, when a language/framework/system has a decision to be made, you have two choices:
1. Present that choice to the user of the system, forcing them to choose 2. Choose the conventional option, hiding away the option (but still allowing for its configuration if they know how/can find it)
intuitively it seems like we should have A062918 < A000127 for sufficiently large n, due to trailing zeros. I'm surprised we still get equalities as high as n = 89.
@Americans: I have the impression this guy from WOP sounds like someone who wants to impersonate an american. Is this a certain accent or does that sound like an "average" american?
> Number of real integers in n-th generation of tree T(2i) defined as follows. Let T* be the infinite tree with root 0 generated by these rules: if p is in T*, then p+1 is in T* and x*p is in T*. Let g(n) be the set of nodes in the n-th generation, so that g(0) = {0}, g(1) = {1}, g(2) = {2,x}, g(3) = {3,2x,x+1,x^2}, etc. Let T(r) be the tree obtained by substituting r for x.
Can you surpass Γ0?
Can you make a function that grows faster than Feferman–Schütte ordinal (a.k.a. Γ0 or φ(1,0,0)) level in the fast growing hierarchy?
For those unfamiliar with what all the above gibberish means, I recommend watching Giroux Studios' video series on the fast growing hierarchy....
@SimplyBeautifulArt this room isn't about PPCG. We do like math around here, so if you wanted to discuss the math or stuff behind it, that's awesome, but for "supporting a PPCG challenge", this really isn't the place
but like, trying to find a faster function should be fairly trivial, right? Like, if I have two functions, f(x) = g(x) and h(x) = g(g(x)), assuming g(x) is strictly increasing, then h(x) >= f(x) for all x, right?
that's why "finding a faster function" is always trivial from a mathematical perspective.
ok, so you've already got a function that grows faster than Γ0. It's still about the bytes, because if you nest that function in itself, it'll grow even faster
@NathanMerrill Sure, but you have to make that function that grows faster than Γ0. If you have a function that doesn't grow fast enough, repeated nesting itself probably won't take it anywhere near Γ0
@LeakyNun a geometric interpretation is that we start with one point at (1, 0)
and at every step we duplicate the points, one goes 1 step to the right, and the other rotates 90 degrees counter clockwise around the origin and scales 2 times
@NathanMerrill If you believe so, I recommend trying to make a function that grows faster than f_ω^ω (n) in the fast growing hierarchy, regardless of byte limitations.
@NathanMerrill That's not what I'm arguing about. I agree its trivial to make a faster growing function, but I do not agree that you can take any function and trivially construct from it a function that grows faster than some other function
@SimplyBeautifulArt Yeah, that's not what Nathan's saying. He's saying that if the challenge is to construct a function f(x) that grows faster than a given g(x), then setting f(x) = g(g(x)) will grow faster than g(x) (assuming that g(x) is strictly increasing).
@El'endiaStarman Yes, I know, but the problem is that you are not given g(x) in my proposed challenge, you have to construct everything from scratch more or less.
I don't mean to 1) complain about women being present on the site or 2) suggest that women could not both be interested in glamour and mathematics, but I've perceived a curious uptick in profiles like this in the past couple of months: profiles with female usernames and glamour- or modeling-type ...
Can you surpass Γ0?
Can you make a function that grows faster than Feferman–Schütte ordinal (a.k.a. Γ0 or φ(1,0,0)) level in the fast growing hierarchy?
For those unfamiliar with what all the above gibberish means, I recommend watching Giroux Studios' video series on the fast growing hierarchy....
