## FANDOM

10,265 Pages

I'm surprised that no one has tried to define this before. This is easy to define, so where's the huge flaw?

## DefinitionEdit

The language of First Order Theory Theory (FOTT) consists of statements, theories, and operators.

In FOTT, a variable is a set. A set is a collection of things, like {1,2,4,8,6,327,pi,Canada,Swiss Cheese,{NO U, THAT IT, CLEAR IT, STOP IT, @person TRIGGERED},...}.

A statement is an operator applied to variables, statements and/or theories (you'll see what theories are later). Here are the basic operators in FOTT:

• a=b is true iff variable a is the same as variable b.
• a∈b is true iff variable a contains variable b.
• ¬(a) is true iff statement a is not true
• (a)∧(b) is true iff statements a and b are true
• ∃a(b) is true iff there doesn't exist a variable a such that statement b is true

Before we define the rest of the operators, we need to define what theories are.

A theory is a system that can create statements by using operators defined for that system. Here is how we can define theories:

S(n|T) (where n is a non-negative integer and T is a theory) represents any statement in theory T, but S(n|T) always represents the same statement. V(n|T) (where n is a non-negative integer and T is a theory) represents any variable in theory T, but V(n|T) always represents the same variable. T(n) (where n is a non-negative integer) represents any theory, but T(n) always represents the same theory. T(n|T) (where n is a non-negative integer and T is a theory) represents any theory in theory T, but T(n|T) always represents the same theory.

φ(S|T) represents statement S in theory T. This can be used to define theories, because we can define the iff operator in FOTT and then make the statement ''φ(S|T) iff [statement]''. For example, we can define a version of ∈ (the X operator) in T(0) by making the statement ''φ(V(0|T(0))X(V(1|T(0))|T(0)) iff V(0|T(0))∈V(1|T(0))'' in FOTT.

Now, here's the catch. First, T(n) > T(m) if n > m. Second, statements, operators and theories in T(n) are also statements, operators and theories in T(m) if T(n) < T(m). Third, a theory can only make statements using statements and operators in that theory. And finally, statements cannot use T(n) unless T(n) is in the second entry of S(n|T), V(n|T), or φ(S|T). Actually, you can.

## Number!Edit

The nth input variable defines what the variable n in a FOTT statement is. For example, if we have the statement 1∈2, the input variables (apple, set of all types of fruits) make the statement true, since apple is a type of fruit, but the input variables (cheese, set of all types of fruits) make the statement false, since cheese is not a type of fruit.

Let 0 = {} and x+1 = x∪{x}. Using this definition of numbers, define FOTT(x) to be the largest value possible that a statement in FOTT x characters long can force the input variable to have so that the statement is true.

Finally, define the number with a 100% totally original name, BIG FOTT, as FOTT10(10100), where FOTT1(x) = FOTT(x) and FOTTy+1(x) = FOTT(FOTTy(x)).