From
∑ilence: The Mathematics of Us

by Sarah B. Royal

The Mathematics of Us

lim (x→∞) f(x)
Not what we become,
but how we behave.
Never reaching our limit.
Our value may not even exist at the point—
commitment without possession.

Love, grief, faith, growth, devotion, aging:
we will continue like this.

∅
Not zero.
Not absence.
Not failure.
Silence that still holds meaning—
an empty room after you leave,
a breath held open,
an equation not yet written.

∑ accumulation
∞ overflow
∎ closure
The proof ends.
The space remains.

limₓ→₀ ∫₀ˣ 1 dx
The accumulated area shrinks to nothing—
motion without residue,
a touch that leaves no scar,
a kindness done quietly.
A beginning
that doesn’t insist on legacy.

∎ (Q.E.D.)
The proof is complete.
Finality. Acceptance.
Love that has been tested.
The moment explanation stops being needed.
Nothing more is required.

0! = 1
Even no steps produce something.
Existence without effort.
Worth without proof.
Love that doesn’t have to begin
to be valid.
ln (1) = 0
No growth. No decay.
Stillness. Contentment.
A heart no longer accelerating.
We exist on both sides.
We break.
Trauma, loss—
we resume, but never the same.

Convergent:
care that completes something.
Divergent:
love that refuses to stop.
Neither is better.
They answer different questions.

Bounded: sustainable devotion.
Unbounded: sacrificial love, obsession, faith.
The tension between us
is where ethical weight lives.
Rearrangement changes the outcome.

Order matters.
Intentions aren’t enough.
Context determines meaning.
The same actions
can heal or harm—
depending on sequence.