🔢 Arithmetization: Encoding Logic as Numbers
Transform mathematical formulas into unique numbers using Gödel numbering
1 Enter a Formula
ℹ️ What is Arithmetization?
Arithmetization is a technique that assigns unique numbers to mathematical symbols and formulas. This allows us to treat statements about mathematics as mathematical objects themselves!
This concept is crucial in proving Gödel’s Incompleteness Theorems and understanding computational complexity.
2 Symbol Encoding Table
Each symbol is assigned a unique prime number:
(
2
)
3
¬
5
∧
7
∨
11
→
13
∀
17
∃
19
x
23
y
29
z
31
0
37
1
41
+
43
=
47