James Ada has posted in several places on the web, his mathematical "proof" for the existence of God using infinity. Here it is in writing and here is his explanation on YouTube video. It's quite clear that he's coming from the Islamic perspective of God, denying the Trinitarian God and the full deity of the Son.
While he posits an interesting exercise, it has fatal flaws both mathematically and theologically.
But his foundational error is believing that one can prove or model the existence of God with a mathematical equation. There is good reason that God prohibited the Old Testament nation of Israel from making any image of Him - i.e., Exodus 20:4-5 and Acts 17:29 say that the Lord is against anyone attempting to make an image of God.
Because God is absolutely unique. He stands alone outside space and time. Scripture is adamant that there is nothing else and no one else like Him. God stands absolutely alone. By definition then, any attempt to model Him using an analogy or model must always fall short. Every analogy is fatally flawed. That does not mean that analogies may not be helpful in understanding some aspect of God - i.e., his power, his creative skill, his sovereignty, etc. But we must be very careful with analogies and models of God and be aware they will always fall short. Nothing can perfectly and accurately model God because He stands alone. He is absolutely unique.
This means if we depend upon a model or analogy for our understanding of God, we inevitably end up with a distorted picture of God at best and an erroneous picture at worst. (This is the mistake that many Christians make in trying to grasp the doctrine of the Trinity.) There is no analogy that can perfectly model God.
But there's also another problem: the transcendence of God. Outside space and time, it is impossible for us to know God apart from his willingness to reveal Himself to us. Had God not chosen to reveal Himself inside space and time to us, we could never know God. Locked in space and time, we can see various powerful evidences for His existence (i.e., cosmology, astronomy, teleology, His workings in history, the basis of morality and ethics, etc.), but we can never know God through them alone.
A beautiful mechanical watch gives indisputable evidence for the existence of the watchmaker and insight into some of his attributes (i.e., his skill, manual dexterity, intelligence, etc.) But by itself, the watch can never give us knowledge of the watchmaker himself - i.e., his name, his location, his age, his height, his education, his sense of humor, his appetite preferences, etc. Similarly the evidences within space and time for the existence of God can never lead us to the knowledge of God Himself.
This means we must necessarily depend on God's revelation to us in space and time to gain true knowledge of Him. God's revelation in Jesus Christ gives us accurate and perfect knowledge of Him ... but not comprehensive. No finite man can ever know everything about the infinite God. We can know Him personally, but not exhaustively, not even in Heaven. This means an exciting, dynamic relationship with Him for all eternity, ever growing in our knowledge of His grace, mercy, love, power, etc.
Back to Ada's "proof".
Infinity is a puzzling concept. As an engineer and physicist, I grow increasingly convinced that God is the only actual infinity and that all other infinities are only "partial" or "potential". An actual infinity is beyond our full comprehension. We can intellectually grasp the concept, but as eternally finite beings we can never comprehensively embrace infinity.
So it is with the amazing one true God who has graciously revealed Himself to us in the Person of Jesus Christ.
"For the scientist who has lived by his faith in the power of reason, the story ends like a bad dream. He has scaled the mountain of ignorance; he is about to conquer the highest peak; as he pulls himself over the final rock, he is greeted by a band of theologians who have been sitting there for centuries."
Robert Jastrow, PhD (1925 – 2008), founder of NASA's Goddard Institute and Director of the Mt. Wilson Institute and Observatories was a renowned American astronomer, physicist and cosmologist.