
7
Well I had to do it at some point.
\(b(a,a)\)
\(a^2\)
\(b(a,a,1)\) \(f_2(a)\)
\(b(a,a,n)\) \(f_{n+1}(a)\)
\(b(a,a,0,1)\) \(f_{\omega}(a)\)
\(b(a,a,n,1)\) \(f_{\omega +n}(a)\)
\(b(a,a,n,k)\) \(f_{\omega k + n}(a)\)
\(b(a,a,0,0,1)\) \(f_{\omega^2}(a)\)
\(b(a,a,n,k,i)\) \(f_{\omega^2 i + \omega k + n}(a)\)
\(b(a,a,0,0,0,1)\) \(f_{\omega^3}(a)\)
\(b(a,a,n,k,l,m)\) \(f_{\omega^3 m + \omega^2 l + \omega k + n}(a)\)
\(b(a,a,b,c,d,e,.....)\) \(f_{...... + \omega^3 e + \omega^2 d + \omega c +b}(a)\)
Limit is \(\omega^\omega\).
\(b(a,a\{1\}1)\) \(f_{\omega^\omega}(a)\)
\(b(a,a,1\{1\}1)\) \(f_{\omega^\omega +1}(a)\)
\(b(a,a,n\{1\}1)\) \(f_{\omega^\omega +n}(a)\)
\(b(a,a,0,1\{1\}1)\) \(f_{\omega^\omega + \omega}(a)\)
\(b(a,a,n,k\{1\}1)\) \(f_{\omega^\omega + \omega k +â€¦
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Work in progress!!!
I was thinking of making some strong ordinal notation to use it to compare functions.I was gonna define it using simpe recursion,but then I thought of Taranovsky's notation which is very strong BECAUSE it's not defined recursively.So I decided to make a very strong using a different aproach than what I usually do.If you're about to comment,please bare in mind that this is just an early version and the reason why I am making this post is because I want to know if the way I described it is welldefined and if it's really what I'm trying to do.Also we should note that it is defined by recursion,so it's limit must be equal to or below \(\omega^{\text{CK}}_1\) and it is probably weaker than Taranovsky's notation.
I wasn't surâ€¦
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Hi again!
Ususally I stick to making my notations as simple as possible,but this time it will get a little complex.To make sure,that I minimalize the amount of mistakes and wrong assumptions I make,I'll start with it simple,but the definitions at the end are going to be more complicated.Like always,if you have any questions or see a mistake in my work,then make sure you tell me in the coments.
Let \(\mathbb{N}\) be the set of all natural numbers.
Let \(\mathbb{Q}\) be the set of all rational numbers.
It all starts from here.
It's not very hard to show that
\(\mathbb{N} \subseteq \mathbb{Q} \Leftrightarrow \mathbb{Q} \supseteq \mathbb{N} \land \mathbb{N} \subset \mathbb{Q} \Leftrightarrow \mathbb{Q} \supset \mathbb{N}\)
Let \(n\) be an element ofâ€¦
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Oh hi!
I finally got around to doing this.Partly because I didn't have much time the last two weeks and partly because I was just lazy.
Now let's come to what I was actually going to talk about.Back when I started doing Googology (or just visiting the wiki) I thought about this function,which produces big numbers by looking at the maximum string you could make by adding every possible arrangement of different "states" of some macine.I'm quoting it because soon after I wrote the basics for the function I realized that you don't need actual "states" for this to work.You just need a finite amount of different....things for it to work.It's very simple and is similar to Friedman's n() function and his word puzzle.It,however,uses a different definiâ€¦
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I have something new today!
And it's big.....It's a whole new theory that could construct very,very large numbers,possibly larger than the current record holder BIG FOOT!
It's MBOT (Mush9Boris Output Theory).
Ok,a while ago Mush9 wrote a blog post about the NOOP FUNCTION,which got me really interasted.
This could possibly beat the largest of numbers ever defined and change the way we think about the creation of numbers.There was no information for the function itself,how it works or what it actualy does.
So I decided to make one myself! On Mush's talk page I wrote a few messages about my idea.It would be very helpfull if you read them before reading this blog post.
MBOT is based off ZF or ZFC.
The thing that is different than in set theory or anâ€¦
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