But you can't reach z0 using addition, multiplication, exponentiation, and ψ(µ) for µ values we've reached. If we reached µ=z0, we wouldn't be needing to take ψ(z0) to begin with...
Why? Well note that you can never exceed an infinite tower of Ω's due to the restriction of addition, multiplication, and exponentiation, and since Ω>ψ(x), we can't make more Ω's that way
@InfiniteMonkey Yes, at the very low levels, we get some fairly obvious Veblen equivalents
That is mind boggling; so as long as two people understand what they mean when creating these they can go on forever, or do we eventually hit an unbreakable wall (unlikely)?
Haha yeah you're right I have no clue yet, I understand just enough to appreciate some what you are showing me here though and that is a lot of fun to be scared by nimbers!
Please help me find the omega limit sets of the following functions in their respective domains:
(1) f(x) = x - x^2 [0,1]->[0,1]
(2) f(x) = 2x -2x^2 [0,1]->[0,1]
(3) f(x) = 3.2x - 3.2x^2 [0,1]->[0,1]
(4) f : R -> R; f4(x) = x^3 + (1/5)x , R is the real numbers
(5) f : [0, 2]-> [0, 2];...
Please help me find the omega limit sets of the following functions in their respective domains:
(1) f(x) = x - x^2 [0,1]->[0,1]
(2) f(x) = 2x -2x^2 [0,1]->[0,1]
(3) f(x) = 3.2x - 3.2x^2 [0,1]->[0,1]
(4) f : R -> R; f4(x) = x^3 + (1/5)x , R is the real numbers
(5) f : [0, 2]-> [0, 2];...
I'm reading a book that claims that this is true. Is there a short/easy proof for this?
This is the Realm of Simply Beautiful…
This is the Realm of Simply Beautiful…