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I come to this topic as a mathematician, not as a philosopher or a theologian. From my perspective, mathematical "sets" — specifically infinite sets — can provide a small insight into the nature of God.
By Robbin O'Leary, Professor of Mathematics
I won't get into the details of the mathematics of Infinite Set Theory now. (Check out https://www.quantamagazine.org/mathematicians-measure-infinities-find-theyre-equal-20170912/
if you want to know the math)
Stated simply, a set is a collection of objects. These objects might be words, numbers or anything we group into that set.
The things we group into sets are called "elements". We will notice right away that some sets are finite, and others are infinite. That is, the elements within some sets have no end, like the elements in the set of all rational numbers, for example.
Theoretical scientists can then treat sets as single objects and do higher form of math to learn things about our reality that couldn't be learned otherwise.
There are some startling findings about Infinite set theory that shed light on some of the concepts found in the bible.
Startling finding #1 - Subtracting elements from an infinite set does not make it smaller.
If you have the set of all numbers, and remove from it, the subset of all even numbers, BOTH the original set AND the subset remain infinite!
Infinity can be taken out of infinity with no reduction in infinity! The same goes for addition. Adding the infinite set of all even numbers to the set of all odd numbers give us a set that is EQUAL in size to the sets added!
Startling finding #2 - Adding infinite sets to infinite sets does not make them any bigger! Infinite sets cannot be reduced OR increased!
Startling finding #3 - Infinite set are all identical. Each element in one infinite set can be paired with elements in another infinite set such that all infinite sets have a 1 to 1 correlation. They are all the same size!
What do these 3 findings mean to Christianity?
Jesus claimed to be God. He said to Thomas, "How can you ask me to show you the Father if you have seen me?" Jesus claimed to have "come out from God". He was calling Himself a proper subset of God.
He shared a 1 to 1 correlation with God, which did not reduce God, or render Jesus Himself less than God. This truth also shows how Jesus could not know some things, and still be God.
God is the absolute infinite set, with The Father, the son, and the Holy Spirit being proper subsets of the set "God".
All three sets are equal. The same size. Each one is equal to God, exactly in a 1 to 1 correlation with God. God does not diminish by removing one subset, or increase when one subset joins the Godhead.
Infinite subsets of infinite sets have a quality called "reflection", which means they have the same qualities of the original set. So as a subset of God, Jesus carries all the qualities of God, and indeed the bible calls Jesus the express image of God, He is the incarnation of God.
Set theory offers an explanation for the inner workings of the trinity.
Mathematicians Measure Infinities and Find They’re Equal
By KEVIN HARTNETT
September 12, 2017
Two mathematicians have proved that two different infinities are equal in size, settling a long-standing question. Their proof rests on a surprising link between the sizes of infinities and the complexity of mathematical theories.
In a breakthrough that disproves decades of conventional wisdom, two mathematicians have shown that two different variants of infinity are actually the same size. The advance touches on one of the most famous and intractable problems in mathematics: whether there exist infinities between the infinite size of the natural numbers and the larger infinite size of the real numbers.
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