So I decided it was better if I showed you the actual content of the blog posts instead of me trying to explain. It also contains Swoop's notations.
A Decagraham isdefined as a 1 followed by a g64 (grahams number) number of zeros.
the Mailucal number is defined as 10^10^10^10^10...10 where the number of ^10's is 10^10^10^10^10.
Franks Number is equal to 10!!!!!!!... where the number of factorial signs exeeds the number of books the library of babel raised to power of itself 65 octillion times.
Kano Loptical Number
The kano Loptical number can be defined as 10 then followed by 10 up arrows then 10.
The MCSICKLE number is defined as 5 followed by 5^5^5^5^5 arrows then 5.
The Wollion is equal to 5 followed by a power tower of googolpex number 6's
The megagoolagon is equal to 1000000000PT (power tower) (999)
Nish's Note: It's empty.
Abraham's number is equal to 666↑↑666
The super silly number is equal to 10↑↑↑10
This number is constructed by the following format 3↑3=3^3 then 3↑ ↑ 3=3^3^3=3^27=7625597484987
3↑↑↑3=3^3^3... where the number of threes in the power tower is 3↑↑3 3↑↑↑↑3=3^3^3... where the number of threes in the tower is 3↑↑↑3 we call this number g1 g2= 3 followed by a g1 number of arrows then 3 you repeated this process until you get down to g3↑↑↑3 then you are finished.
squid number 1
To obtain the Squid number you first start with 10 like so you then raise it to the power of ten like so 10^10 after that you raise that to the power of ten like 10^10^10. You repeat this until you have ten 10^'s like so 10^10^10^10^10^10^10^10^10^10 now although this number is big it is knowhere near the squids number.
You then repeat this 10^10^10^10^10^10^10^10^10^10 times.
you then repeat the process of repeating 10^10^10^10^10^10^10^10^10^10 that many times.
This is squids Number.
Tomb number is equal to 10↑↑↑↑↑↑↑...↑↑↑↑↑↑↑10 where the number of arrows is equal to grahams number.
This is equal to 5↑ ↑ ↑ ↑ ...↑ ↑ ↑ ↑ 5 where the number of arrows is 5↑ ↑ ↑ ↑ 5.
A Frogillion is found the same way Grahams number is found only my number is a lot lot bigger than Grahams. you start with G64(grahams number)you then take 3 place g64 number of arrows to get g65 you repeat this process until you get to gg64 or g grahams number.
to obtain this number you first take the number of ways to arrange 6 objects 720=6!-=6*5*4*3*2*1
you then take 6! and factorial that number (720) to get 6!!
you then take 6!! and double how many factorial signs they are to make 6!!!!
you then add another ! sign to make 6!!!!!
after that you double the number of !'s again to get 6!!!!!!!! you then repeated this process of doubling the number of ! signs until you have doubled it 2^10^20^40^80^7687 number of times. Now that's big.
I have decided to define a Tetrallion as 4^4^4^4 raised to the power of 4 where the number of ^4's is 4^4^4^4.
Although this definition is short it is the best I could come up with at the time of writing this.
To construct this number you first start with ten you then multiply it by ten to get 100 after that you multiply the 100 you got previously to get ten thousand you then multiply the ten thousand by ten thousand to get 100 million you multiply the 100 million by 100million to 10 quadrillion you then multiply ten quadrillion by quadrillion to get 100 nonillion or ten to the 32 you then square that number to 10^64 you square that number to get 10^128 you square it again to get 10^256 you square it again to get 10^512 you square it again to get 10^1024 you square it again to get 10^2048. You then move on from squaring and start raising it to the power of 4 and no this isn't a typo.After you raise the number you got previously to the power of 4 you get10^8192 you then raise that number to the power of 4 to get 10^32768 you then raise that number to the power of 4 to get 10^65536 you then raise this number to the power of 4 to get 10^262144 you raise that to power of 4 to get10^1048576.Now once you've got that number you don't raise it to the power of 8 you raise it to power of 16 to get 10^16777216 you then raise that number to the power of 16 to get 10^268435456 you then raise that to the power of 16 to get 10^42944967296 you then raise this number not to the power of 32 or even the power of 64 not even the power of 128 no you raise it to the power of 256. so after you do that you get 10^1099511627776 you then raise that to power of 16 to get 10^2184749767107x10^14 so just over ten to 200 trillion. You then raise that number to power of 65536 to get 10^1.844674407371x10^17 to then raise that number to the power of 2^10^10^64 you raise that number to power of 2^10^10^10^10^10^10^10^10^10^10... where the number of ^10's is 2^10^10^64. you then take that number and exponentiate it 2^10^10^64 times but this isn't even the start of this number you then repeat this process process 2^10^10^64 times. But you aren't finnished yet you then have to raise it to the power of 2^10^10^10^10^10^10^10^10^10^10^10....^64 where the number of ^10's is 2^10^10^10^10^10^10^10...10^64 where the number of 10^'s is 2^10^10^10^10^10^10^64 you then this repeat 10^10^10^10^64 times then repeat again another 10^10^10^10^64 times. You then repeat the process 10^10^10^10^10^10^64
In total you have to repeat it 10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^10^64 times.
Once you've done that your finnished.
my first attempt at creating notation.
Well seeing as people have been saying I should create my own notation I have decided to give it a go.
I call it swoops notation you start with n where n= a positive integer say 5 the next level above that is n-p this means n raised to itself p times so if n=5 and p=6 then n-p=5^5^5^5^5^5^5 or 5 followed by a tower of 6 5's. above that is n-p-o this means that you repeat the n-p operation o times. For example if n-p=5^5^5^5^5^5^5 and o=10 you repeat the n-p operation 10 times giving you a tower of 60 5's after that base number 5. Above that is the n-p-o-(x)this means that you repeat the n-p-o operation x times this means that if n-p-o =5 followed by a tower of 60 5's and (x)=100 you raise the number of things in the tower to that value (x)by this I don't mean that you have 6000 5's in the tower no you have 60^100 things. But we can go further than that n-p-o-(x)-(y) this means that you repeat the n-p-o-(x) operation for (y)times where (y)is a number greater than an tower of exponents n-p-o-(x) high then repeated that many times for n-p-o-(x)cycles. How good is this notation.
This is the a new type of notation that I have decided to name swoops notation ii as in 2.
To start off you take n and like before this equals a positive integer.
so for example n could 10
you then place parentheses around the number you have chosen for n l so for example 10 would be (10)
By doing this you raise it to the power of itself of n times so for (10) you get 10^10^10^10^10^10^10^10^10^10.
you then place double parentheses around the number this means that you repeat the (10) operation that many times.
so that means that if you have a tower that looks like this 10^10^10^10^10^10^10^10^10^10 you literally copy and paste this that many times making a gigantic tower.
Triple brackets means that you repeat the double bracket operation double bracket number of times to make an even bigger tower
quadruple brackets means that you repeat the triple bracket operation triple up times.
And so and so forth.
Improved version of swoops notation.
Improved version of swoops notation
This is the improved version of my 1st notation mainly n-p-o-(x)-(y)
For this improved version we start like this (n) this means that you take (n) and make a power tower of (n) height.
so if n=2 then you get 2^2^2 although this looks like a tower of 3 2's the base ie the 1st 2 doesn't count.
(n)-(p) means that you repeat the (n) operation) (n) times you then repeat that another (n) times then repeat that another (n) times so in total you repeat this process (n) times.
by repeat I mean that you literally copy and past that tower you got from your starting number n and copy that power tower that many times. so for you would copy and paste 2^2^2 2^2^2 times you repeat the process that many times.
(n)-(p)-(o) means take what you did for (n)-(p) and repeat it (n)-(p)^(n)-(p)... times where the number of (n)-(p)'s is equal
The next stage is to place the ((x)) in the notation what this does is that it repeats what you did in the previous stage and raises it to a power tower of itself , itself many times.
For example so suppose you have a tower with a height 6*10^180 you repeat the process of what I called extending and repeat it that many times and do that many cycles of repeats.
now for the final part of the notation the ((y)) raises the number you got previously to the power of itself that many times and you repeat it that many times for that many cycles you then repeat this processthat many times and so and so and so forth until you have repeated the process that many times.
Once you've done that you're finnished.
Although I Have by people in the comments not to use up arrows I feel like I have to express this number in a way that will get people to see just how big it is so here go's.
you start with 10↑10 or in layman's terms 10^10 You then place 10↑10 number of arrows between the tens. you then put that many arrows between the 10's After that you repeat it 10↑↑↑↑10 times.
Nish's Note: It's empty.
This number is defined using my swoops notation as (10000)-(20000)-(40000)-((500))-((1000)).
Review of operators from successor function to tetration.
Although people have been saying in the comments that I should just stick to my previous notations I personally feel that I won't be satisfied with the notation until it is absolutely perfect with no chances of confusing any one.
To start off I am going to review what I would call the genesis operators of googology mainly addition and multiplication although this may seem like a waste of time I feel that it is essential for my notation.
Before we start off with that we are going to review the successor function mainly s(n)=n+1
examples of the successor function are s(1)=2
Moving onto addition the 2nd most simple operator it represents the sum of two numbers.
An example of addition is the classic 1+1 featured in various jokes
Another is Also the first operator that could be classed as a googolism as you can get some pretty big numbers just with addition.
The next level above that is multiplication this is repeated addittion so for example 3*3=9 or 3+3+3 as there or 3 lots of 3.
Beyond that we get to exponents this is repeated multiplication of the same number by itself.
we denote this as x^y
An example of this is 2^10=1024 this means that you multiply 2 by itself 10 times.
Beyond that we get to tetration or repeated exponents.
an example of tetration is;
2^2^2 this means take two raise it to the power of two to make four you then take that number and raise it to power of 4 to make 16.
Another example of tetration is 10^(10^10) or ten raised to the power of ten billion.
Hopefully I explained it fairly well.
I have decided to invent a brand new number that will be bigger than any number I have written about so far.
I have decided to call it Lauffer number of the 1st kind.
Lauffers number follows my swoops notation in its construction mainly (n)-(p)-(o)-((x))
Here are the instructions or as I like to call them the recipe for making this number.
step 1: begin (n) make it equal to 1000 followed by a power tower of 1000 1000's
In other words there is a tower of 1000 1000's stacked onto the base number 1000.
Like this: 1000^1000^1000^1000^1000^1000..^1000 (1000 1000's in the tower not including the first 1000)
Once you have got that out of the way you move onto the (p) function what this does is raises the number you got previously to the power of itself you then repeat this process again you then raise that number to the power of itself. you then raise that number to power of itself you repeat the process of raising of repeating and raising to the power of itself (n) times in other words you have to repeat the process I just described that ridiculous number you started with number of times. now that completes the 1st half of the process the next part is to incorporate the (o) into the notation what this does is that it repeats what you did for (p) (n)-(p) times making a number so large it transcends the imagination literally. But that isn't the end you now have to incorporate the dreaded ((x)) what this does is that it repeats what you did for o (n)-(p)-(o) times wow now thats big.
So there you have it Lauffers number or in other words a one way ticket into madness.
I would like to know what people think about this number as well as how well it would stand against other numbers on the wiki.
Lauffers number of the 2nd kind.
Presuming that you have seen my Lauffers number of the first kind it is now time to go on to the second kind.
As usual we use swoops notation mainly (n)-(p)-(o)-((x)
We make (n)=1000000 followed by a power tower of 1 million 1 millions In other words there is a tower of 1 million 1 millions stacked onto the base number 1 million or in other words the first milllion. This process is the same as the last Lauffers number only instead of one thousand we use million. once you have got that tower of 1 million 1 millions stacked onto the base number one million you now incorporate the (p) into the notation. What this does is that it raises the number you got previously to the power of itself you then repeat the process you then raise that number to power of itself you continue this process of raising to power of itself and repeating (n) times.Or in other words you repeat the process I just described before (n) times.Next up we need to incorporate the (o) what this does is that it repeats what you did for (p) (n)-(p) times making a number so large that if you try to imagine it your head will implode into a black hole.But you aren't finnished yet you now have to incorporate the dreaded ((x)) into the notation what this does is that it repeats what you did for (o) (n)-(p)-(o) times now thats huge!
So there you have it Lauffers number of the 2nd kind a number that makes Lauffers number of the 1st kind look like a proton in the multiverse.
Side note: I would like to know what people think about this number as well as a general comparison to other numbers to see how big it is I would also like to know what you think about the notation?
Leave a comment down below.
So I have decided to invent a new number called forts number I define it as (n) as in the (n) from my swoops notation where (n)= 1 billion with a tower of 1 billion 1 billions following it. 1000,000,000^1000,0000,0000^1000,0000,000...(1 billion ^ 1 billion minus the first billion.) The reason for this number is simply because I liked the look of it and nothing else.
Lauffers number of the 3rd kind.
Today I am going to reveal the 3rd number in the Lauffer sequence to construct this number we of course must use swoops notation (n)-(p)-(o)-((x))
We denote (n) to equal 1 trillion^trillion^trillion^trillion^trillion...(1 trillion 1 trillion to the power of 1 trillion following the first trillion you write down.) In other words you starts with 1 trillion and you write a tower of 1 trillion 1 trillions after it how simple could that be. we then integrate (p) into the number what this does is that (n) to the power of (n) (n) times to get a better glimpse into what this means read my other blogs on the lauffer sequence. Next we include the (o) what this does is repeats what you did for (p) (n)-(p) times. Finally we include the ((x)) what this does is that it repeats what you did for (o) (n)-(p)-(o) times.
Attempting to redesign my notation.
I have been told in the comments that my swoops notation has some problems so to do this I will attempt yet again to improve it if this improvement fails then I will improve it again. to start off I am going to just use exponents for my numbers this way I can get large numbers without using confusing notation.
10^100=1 followed by 100 zeros
10^1000=1 followed by 1000 zeros
2^256=2 multiplied by itself 256 times
3^4567=3 multiplied by itself 4567 times.
4^4=4 times itself 4 times.
10^12500=10 multiplied by itself 12500 times.
33^3333=33 multiplied by itself 3333 times.
10^(googol)=10 multiplied by itself a googol times.
10^(googolplex)=10 multiplied by itself a googol times.
10^(rayos number)-10 multiplied by itself rayos number of times.
Although these aren't original ideas of mine and some could be called naive extensions or salad numbers I personally feel that it is essential for me to go back to basic googolisms before starting to create my own notation.
If you have any suggestions as to how I could improve my notation feel free tell me you can also ask questions and I will try to explain.