Propertus is a very large concept, coined by Spelpotatis. It will also be the start of spels S1(number) series of defintion indexes.
Definition[]
Definition of a property[]
A property is some conditon some number can satisfy. For example, "This number is 3" is a property, and "This number is not 3" in also a property. properties can also be more complex, like "This is not the least number of any property", which for the record is the definition of conkept, and this definition is very paradoxical but this is fictional googology after all.
How to find if two properties mean different things[]
If two properties imply the same thing, it's denoted by A = B, where A and B are two properties that both mean the smae thing.
If they don't, we say A != B.
Finding out if two properties are the same is quite simple. If there is any number or object that is different when posessing A as if it was to be defined as posessing B, then A != B.
Sub-Propertus[]
This is the first stage of propertus. It is defined as the klongest sequence A != B != C != D !=... you could possibly make. A easier way to think of it is just the amount of properties that are different from each other.
Propertus[]
Here comes the real number. This is the same as Sub-Propertus, but we change the defintion of property from something a number can satisfy to something any object in general can satisfy. For example, "This object is a box" is now a property, even though there is no number or mathematical concept that fulfills it.
Size[]
If two numbers satisfy all the same properties, they must be the same number (There is no property the first number satisfy the other number doesn't.). The proof of this is trivial.
This means you could map every number to a set of unique properties. This means the amount of properties that exist and the amount of numbers that exist are almost the same. I say almost, because there can of course be multiple numbers that have some shared properties. However, fact still is that if you have too few properties, you won't be able to describe an amount of numbers that streatches the entire extended fictional number line. This means that propertus is basically larger than every number that has been defined before this.
I don't relaly know if this is legal or not considering it's just a clever rewriting of "past every number", but i guess that was the goal for making a big number anyways so yay?