Y’know I’m bored time to make a stupidly large number.
Rennison’s number
Alright so let me create a method called the “Tropical Forest Method” that we will use to make the biggest number ever… something that operates through various symbols and the Kruskal’s Tree Theorem… we’ll use emojis to represent it:
Repeatable commands:
🍃 - +1
☘️ - Increased to the power of 3
🍀 - increased to the power of 4
🌲 - Adds 1 node colour to tree structure
🌳 - Doubles the node colours of tree structure
🌴 - Makes every individual node worth what the entire structure was (includes +1 bits)
How many times over (applied to all actions)
- X1
🍂 - X2
🍁 - X10
🌱 - X100
🪴 - X1000
🌹 - X1 Million
🌷 - X1 Billion
💐 - X1 Decillion
⭐️ - XGoogol
🌺 - X1 Centillion
🌟 - XGoogolplex
💫 - XGoogolplexian
✨ - XGrahams Number
🌌 - XRayo’s Number
If anyone is unaware, basically a Googol is (10^100) in size, 1 followed by 100 0s, now a Googolplex is (10^Googol), it has a Googol 0s, and a Googolplexian is (10^Googolplex), you get the point they are large… however for calculating Rennison’s number they are completely worthless and add nothing. Same goes for Graham’s number, which while large, becomes obsolete fast as early as the third three colour node.
The real bearing ultimately comes from the trees, which I will explain. Basically Kruskal’s Tree Theorem operates as a game of making trees, you place down coloured nodes, starting with 1 node and going up 1 each time, however you cannot create the same pattern twice. So like when you place a colour at your first tree you can’t use that colour again since that colour is now recognised as a used pattern, then using two of the same colour at the second tree when you have 2 means you can use that colour but can’t connect 2 together… however if you were to say use 4 of the same colour at the fourth tree, then you can still use 3 or 2 of that colour connected now infinitely, and if you connected 2 of the same together and one of those 2 to a different colour at the third tree then you can’t connect 2 of that same to that other but you can’t still connect the different colours together and the same colours together… if that makes sense.
You start with 1 colour, this is TREE (1), and in it you can only do 1 node since you’ve already wasted it, TREE (2) adds a colour however still stops at the second tree as you expend 1 colour the first tree and connecting the second colour together means you can’t do it again… TREE (3) however, with one added colour opens so much variety that completing every variation would take longer than we can calculate… so, TREE (3) is also known to be one of the longest numbers ever conceived… however not quite the longest.
Rayo’s number is defined as being “The smallest number bigger than any finite number named by an expression in any language of first-order set theory in which the language uses only a googol symbols or less.”, which… in non mathematical terms is basically saying “One above everything we can calculate”… everything else we’ve been looking at has nothing on this, and so this is the modifier that will be used for Rennison’s number.
Anyways… enough serious math, ready to see the largest number ever? Okay:
🌌🌲🌳🌴
That’s it, that’s Rennison’s number… want to know why this is so large? Well let me put it this way… each action has XRayo’s number added to it… so in reality the game immediately jumps to TREE (Rayo’s Number)… doubled by 2, but WAIT, no the 2 is X by Rayo’s number so it’s actually X by Rayo’s number X2, then after all this you add the palm layer which makes every individual node worth what the entire structure was previously… X by Rayo’s number so you actually now already have Rayo’s number layers of this whole process by round 2… of all Rayo’s number of rounds of this rapidly multiplying again and again… the result, my friends, is Rennison’s number.
Understood any of that? No, well fair enough… but yeah this is big. I’ll be honest considering I conceptualised this post as a joke I’m surprised how sophisticated I ended up getting… either way say hello to… Rennison’s Number, it’s really large… and stuff.
BTW if you’re wondering what all the other random commands I added to the tropical method are for, idk I just thought it looked cooler.
