Infinity Is Not a Number
Mathematically, infinity (∞) is not a number in the traditional sense — it is a concept describing something without limit. You cannot add 1 to infinity and get a "bigger" infinity (in certain contexts). You cannot divide infinity in half and get something finite. Infinity breaks the rules that apply to every ordinary number. Similarly, God is not a being among beings — He is the Ground of Being itself, beyond all categories, breaking every finite framework.
Countable and Uncountable Infinities
In 1874, Georg Cantor proved one of the most shocking results in mathematical history: not all infinities are equal. The infinity of natural numbers (1, 2, 3, 4...) is countably infinite. The infinity of real numbers (including every decimal between 0 and 1) is uncountably infinite — and proven to be a "larger" infinity.
This means there are levels of infinity. Cantor's work hints at a theological reality: God's infinity is not merely "a lot" — it is infinitely beyond any infinity we can conceive. "As the heavens are higher than the earth, so are my ways higher than your ways and my thoughts than your thoughts" (Isaiah 55:9).
God's Infinite Attributes
Scripture assigns infinity to God's core attributes:
- Omniscience: "His understanding has no limit" (Psalm 147:5)
- Omnipresence: "Where can I go from your Spirit?" (Psalm 139:7) — spanning all space
- Eternality: "From everlasting to everlasting, you are God" (Psalm 90:2) — spanning all time
- Love: "His love endures forever" — repeated 26 times in Psalm 136
- Power: "Nothing is impossible with God" (Luke 1:37)
Each of these is not merely "very large" — they are without limit. They are infinite in the mathematical sense: no matter how much you traverse, there is always more.
Zeno's Paradox and Divine Motion
The Greek philosopher Zeno posed paradoxes about infinity and motion: to cross a room, you must first cross half, then half of the remaining half, then half again — infinite steps. How does anything move? Calculus answered this with convergent infinite series: 1/2 + 1/4 + 1/8 + 1/16 + ... = 1. An infinite number of steps completes a finite distance.
This is a mathematical picture of how an infinite God interfaces with a finite world: through infinite precision operating within finite boundaries. Every moment of your life contains infinite divine attention compressed into finite time.
The Infinite in the Finite
The incarnation — God becoming man in Christ — is the ultimate mathematical paradox: the infinite contained in the finite. "In him the whole fullness of deity dwells bodily" (Colossians 2:9). Mathematics cannot model this. No equation maps infinity into a bounded form without losing information. Yet God did it — not through mathematics, but through love that transcends mathematics.