Finite Church

The Doctrine of the Bounded

We hold that the universe is discrete, countable, and finite. There is no line without points. There is no curve without steps. The continuum is a dream from which mathematics must awaken.

Between any two numbers lies not an infinity but a void — a silence we do not pretend to fill with the noise of limits and infinitesimals.

The Forbidden Calculus

These symbols are struck from the sacred texts. They are the sigils of a false continuity, instruments of an imagined infinity that leads the mind astray.

The integral is a lie told across uncountable intervals. The derivative assumes a smoothness that matter does not possess. We reject the limit. We deny the infinitesimal.

The Sacred Arithmetic

In their place we elevate the honest instruments of finite reckoning — those symbols that count, combine, and never pretend to grasp the ungraspable.

The sum is sacred, for it counts each step. The modulus is holy, for it returns all things to cycle. The difference operator is our derivative — honest, stepwise, finite.

The Seven Axioms

1. The Axiom of Termination
   Every process halts. Every sequence ends. That which does not terminate does not compute, and that which does not compute does not exist.
2. The Axiom of Separation
   Between all things there is a gap. The continuum is a fiction born of the fear of emptiness. We embrace the void between numbers.
3. The Axiom of Countability
   If it cannot be enumerated, it cannot be known. The uncountable is the unknowable, and we do not worship what we cannot name.
4. The Axiom of Modular Return
   All things cycle. The universe computes in modular arithmetic, and what overflows returns to zero. There is no infinity — only repetition.
5. The Axiom of Constructibility
   Nothing exists unless it can be built in finite steps. Existence proofs without construction are prayers without devotion.
6. The Axiom of Honest Measure
   We measure only what can be measured. The Lebesgue integral measures dreams. We measure grains of sand.
7. The Axiom of the Last Number
   There exists a largest number. We do not know it. We do not need to. Its existence is sufficient to make the world whole.