# Infinite Set Theory Explains The Trinity

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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.

I am going to respond as a math aficionado, not an atheist:

Startling finding #1 - Subtracting elements from an infinite set does not make it smaller.

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!
All of these findings (you may be startled to find), are incorrect, strictly speaking. Starting with #3, the referenced paper does not prove that all identical sets are equal, but rather that to specific infinite sets, p and t, have the same cardinality. Cantor's diagonal argument still holds to demonstrate that the Real numbers are a larger cardinality than countable sets.

As a consequence, findings #2 and #1 are also false, as you can move from a countable set to an uncountable set via addition or subtraction. For example, the Integers + (Reals-Integers) = Reals. E.g. you've added something to a countable set to make it uncountable, thus increasing its cardinality. And a similar logic shows that you can subtract from an uncountable set to make it countable, thus decreasing its cardinality.

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.
Presuming that the set God is a countably infinite set, and the sets Father, Son, and Holy Spirit are proper subsets that are also countably infinite, then |G| = |F| = |S| = |H|.

That they exist in 1:1 coorelation with God (and each other) is true.

However, it is not true to say that the sets are "equal." They have the same cardinality, yes, but sets are only equal if they contain the same elements. Since F, S, and H are all proper subsets of G, then necessarily G contains elements not in F, S, and H meaning it is not equal to them. It is possible for F = S = H, however, since we are told of no other distinguishing characteristics that might set them apart.

Infinite subsets of infinite sets have a quality called "reflection", which means they have the same qualities of the original set.
I confess that I do not know much about the Reflection property, but as far as I can tell, it is an existential statement. That given some set (or collection of sets) with some property, that there exists a subset that also contains that property. It does not (as far as I can tell) state that any subset must also have that property.

"Property" seems to be ill defined, so this is hard to evaluate. But again, it would seem that the fact that G contains elements not in F, S, or H, then G has properties that are also not in F, S, H, namely the property of containing said elements!
--> @drafterman
I am going to respond as a math aficionado, not an atheist:
Thank goodness! I just got assigned a duty by Mrs. Ethan so I'll reply later. Good post.
There are several different kinds of infinities and some are - contrary to common sense (but consistent with logic) - "larger" than others, for lack of a better term.

There is a YouTube channel by the name of Numberphile that made a good series of videos on the topic a long time ago that I will try to dig up (and I will give up if I can't find it in the first minute or so because they have made a lot of videos over the years).

The channel itself is hosted by a collection of actual mathematicians and the occasional physicist or two that explain complex mathematical concepts in ways that laymen can (usually) understand. They actually know what they are talking about, not just copy pasting random info from search engines like some "education" channels.
--> @Discipulus_Didicit @drafterman
All of these findings (you may be startled to find), are incorrect, strictly speaking.
Not so. But let's look at them.

Starting with #3, the referenced paper does not prove that all identical sets are equal,
The paper does not try to prove all identical sets are equal! What would "identical" and "equal" mean in such a case? Identical sets ARE equal.

The paper asserted that though p was a subset of t, t was not larger than p! The subset still shared a 1 to 1 correlation with the original set. They were both infinite.

but rather that to specific infinite sets, p and t, have the same cardinality. Cantor's diagonal argument still holds to demonstrate that the Real numbers are a larger cardinality than countable sets.
True, and I touch on that later.

As a consequence, findings #2 and #1 are also false, as you can move from a countable set to an uncountable set via addition or subtraction. For example, the Integers + (Reals-Integers) = Reals. E.g. you've added something to a countable set to make it uncountable, thus increasing its cardinality. And a similar logic shows that you can subtract from an uncountable set to make it countable, thus decreasing its cardinality.
You are confusing countability with infinity. You cannot move from infinity to finite via subtraction with infinite sets. And addition does not change a sets cardinality. Findings #1 and #2 are correct as to the sets quality of being infinite.

Presuming that the set God is a countably infinite set, and the sets Father, Son, and Holy Spirit are proper subsets that are also countably infinite, then |G| = |F| = |S| = |H|.
Thank you.

That they exist in 1:1 correlation with God (and each other) is true.
And any being with a 1 to 1 correlation  with God IS God.

However, it is not true to say that the sets are "equal." They have the same cardinality, yes, but sets are only equal if they contain the same elements.
Untrue. Two sets containing all the same elements are tautology. They would be the same set. They are equal in "infiniteness". And share cardinality.

Since F, S, and H are all proper subsets of G, then necessarily G contains elements not in F, S, and H meaning it is not equal to them.
Partly true. For F, S and H are still just as "big" as G, and still have a  1 to 1 correlation to G. And while G has elements not in each subset, no subset has elements not in G.

It is possible for F = S = H, however, since we are told of no other distinguishing characteristics that might set them apart.
If they are separate sets, they must have at least some unique elements.

But again, it would seem that the fact that G contains elements not in F, S, or H, then G has properties that are also not in F, S, H, namely the property of containing said elements!
Containing certain elements is not a "property". Of course G has elements not in a subset. That is a given. The point is that the subset is still the same size as G.

There are several different kinds of infinities and some are - contrary to common sense (but consistent with logic) - "larger" than others, for lack of a better term.
Yes, but I wanted to ease into that. An absolute infinity has elements which are continuous and therefore uncountable. God is an absolute infinity.

As the bible says..

2Ch 6:18 - “.... The heavens, even the highest heavens, cannot contain [God].

And as Cantor showed, each subset of an absolute infinite set is itself an absolute infinity. God is like infinities within infinities. Like fractals.

This is what the bible is talking about when it says,

Rom 1:20 - For since the creation of the world His invisible attributes are clearly seen, being understood by the things that are made, even His eternal power and Godhead, so that they are without excuse,

Infinite set theory explains the trinitarian nature of God, and how the subsets work in and relate to, the superset God.

Heb 1:3 - Who being the brightness of his glory, and the express image of his person, and upholding all things by the word of his power, when he had by himself purged our sins, sat down on the right hand of the Majesty on high.
--> @ethang5
Starting with #3, the referenced paper does not prove that all identical sets are equal,
The paper does not try to prove all identical sets are equal! What would "identical" and "equal" mean in such a case? Identical sets ARE equal.

The paper asserted that though p was a subset of t, t was not larger than p! The subset still shared a 1 to 1 correlation with the original set. They were both infinite.
Sorry, I meant "infinite", not "identical"

As a consequence, findings #2 and #1 are also false, as you can move from a countable set to an uncountable set via addition or subtraction. For example, the Integers + (Reals-Integers) = Reals. E.g. you've added something to a countable set to make it uncountable, thus increasing its cardinality. And a similar logic shows that you can subtract from an uncountable set to make it countable, thus decreasing its cardinality.
You are confusing countability with infinity. You cannot move from infinity to finite via subtraction with infinite sets. And addition does not change a sets cardinality. Findings #1 and #2 are correct as to the sets quality of being infinite.
"Countable" is a kind of infinity. And there are different infinities with different cardinalities that allow is to make statements regarding their size. The size of a set is represented by its cardinality. And you an certainly (as shown) move between larger and smaller cardinalities among sets of infinite size through addition and substraction.

That they exist in 1:1 correlation with God (and each other) is true.
And any being with a 1 to 1 correlation  with God IS God.
No, being in 1:1 correlation with something does not make those two things identical. The set of all even numbers is in 1:1 correlation with the set of odd numbers, but it would be incorrect to say that the set of even numbers IS the set of odd numbers.

However, it is not true to say that the sets are "equal." They have the same cardinality, yes, but sets are only equal if they contain the same elements.
Untrue. Two sets containing all the same elements are tautology. They would be the same set. They are equal in "infiniteness". And share cardinality.
But that is not what makes sets equal. Sets are only equal of they contain the same elements.

Since F, S, and H are all proper subsets of G, then necessarily G contains elements not in F, S, and H meaning it is not equal to them.
Partly true. For F, S and H are still just as "big" as G, and still have a  1 to 1 correlation to G. And while G has elements not in each subset, no subset has elements not in G.

It is possible for F = S = H, however, since we are told of no other distinguishing characteristics that might set them apart.
If they are separate sets, they must have at least some unique elements.

But again, it would seem that the fact that G contains elements not in F, S, or H, then G has properties that are also not in F, S, H, namely the property of containing said elements!
Containing certain elements is not a "property". Of course G has elements not in a subset. That is a given. The point is that the subset is still the same size as G.
In this respect we were talking about reflection which talks about the properties of sets. What do you consider to be "properties" of sets in the context of the reflection principle?

--> @drafterman
The size of a set is represented by its cardinality. And you an certainly (as shown) move between larger and smaller cardinalities among sets of infinite size through addition and substraction.
The only way to reduce an infinite set in size is to subtract an infinity, but that is not subtraction as much as it is a deletion.

No, being in 1:1 correlation with something does not make those two things identical.
It makes them identical in infiniteness.

The set of all even numbers is in 1:1 correlation with the set of odd numbers, but it would be incorrect to say that the set of even numbers IS the set of odd numbers.
You misunderstand me. A set that shares a 1 to 1 correlation with another set that is infinite, is itself infinite. And while we have infinite sets in theory, God is the only literal infinite set. Any real set that is infinite is either a subset of God, and therefore reflects the property of God, or it is the superset God itself.

But that is not what makes sets equal. Sets are only equal of they contain the same elements.
No. There are several ways sets can be equal. They can have an equal number of elements, or they can have the same type of element, or they can be infinite.

It is not rational to say two sets are equal because they have the same elements. This is tautology. Its like saying the set of all even numbers is equal to the set of even numbers. They aren't two separate sets. But sets can be equal in size, or type of S, or in infinity.

In this respect we were talking about reflection which talks about the properties of sets. What do you consider to be "properties" of sets in the context of the reflection principle?
Fantastic question! Elements are placed into sets because they share a property. For example, a car in the subset of the Set of Red Cars in America will be red. Red can be  considered a "property" of the main set that will be reflected in any subset.

So any subset (F, S, H) of the superset G will reflect the property of Godhood found in the superset.

Jesus said, "I and my Father are one." He meant that He shared the property with  the Father. That property is only shared by members of the superset G.
--> @ethang5
The size of a set is represented by its cardinality. And you an certainly (as shown) move between larger and smaller cardinalities among sets of infinite size through addition and substraction.
The only way to reduce an infinite set in size is to subtract an infinity, but that is not subtraction as much as it is a deletion.
Whatever you want to call it, it is the process you described.

No, being in 1:1 correlation with something does not make those two things identical.
It makes them identical in infiniteness.
It makes their cardinality the same, yes, but it does not make them equal.

The set of all even numbers is in 1:1 correlation with the set of odd numbers, but it would be incorrect to say that the set of even numbers IS the set of odd numbers.
You misunderstand me. A set that shares a 1 to 1 correlation with another set that is infinite, is itself infinite. And while we have infinite sets in theory, God is the only literal infinite set. Any real set that is infinite is either a subset of God, and therefore reflects the property of God, or it is the superset God itself.
What property of God?

But that is not what makes sets equal. Sets are only equal of they contain the same elements.
No. There are several ways sets can be equal. They can have an equal number of elements, or they can have the same type of element, or they can be infinite.
Not in set theory, no.

It is not rational to say two sets are equal because they have the same elements. This is tautology. Its like saying the set of all even numbers is equal to the set of even numbers. They aren't two separate sets. But sets can be equal in size, or type of S, or in infinity.
You aren't always dealing with known sets. Sometimes you have two sets that may be different that are subsequently shown to be equal. That is: containing exactly the same elements. This is a very useful thing to do in set theory.
--> @drafterman
Not in set theory, no.
Sorry, I don't understand what you're opposing. Are you saying that two sets with the same number of elements cannot be called equal?

It makes their cardinality the same, yes, but it does not make them equal.
It depends on what the equality refers to. Two infinite sets are equal in infinity if they share a 1 to 1 correlation. Also, two sets with similar element types can be said to be "equal", like a set of black cars, and the set of red cars, if "equal" is referring to the type of element within the sets.

You aren't always dealing with known sets. Sometimes you have two sets that may be different that are subsequently shown to be equal. That is: containing exactly the same elements.
Then you should say,
"Sometimes you have two sets that are [thought to be] different...

What property of God?
Infiniteness, omniscience, omnipotence, omnipresence, immutability.

The divine properties.

--> @ethang5
Not in set theory, no.
Sorry, I don't understand what you're opposing. Are you saying that two sets with the same number of elements cannot be called equal?
Not if those elements are different.

{1,2,4} is not equal to {1,2,5}
The set of even numbers it not equal to the set of odd numbers.

It makes their cardinality the same, yes, but it does not make them equal.
It depends on what the equality refers to. Two infinite sets are equal in infinity if they share a 1 to 1 correlation. Also, two sets with similar element types can be said to be "equal", like a set of black cars, and the set of red cars, if "equal" is referring to the type of element within the sets.
Since we're dealing with set theory, we should use the terminology of set theory. I'm not aware of the measure: "equal in infinity" unless you're just using that as a place holder for "cardinality." But the cardinality of the set is also its size, so we need to look back at the statement you made:

"All three sets are equal. The same size."

So either you are being redundant and saying that they are the same cardinality twice, in two different ways, or you have made an incorrect statement.
Janethang65.
Trying to believe in this trinity sure does look painful.

I highly doubt anyone can believe in God 83%
Ethang is like 63% believes in god

Half Arsed Theists .   HAT

Good game.
Good game.

--> @drafterman
Not if those elements are different.
Can the number of elements be equal?

The set of even numbers it not equal to the set of odd numbers.
They are equal in the number of elements.

Since we're dealing with set theory, we should use the terminology of set theory.
I'm trying to use set theory to explain the trinity, I think some flexibility is justified here.

So either you are being redundant and saying that they are the same cardinality twice, in two different ways, or you have made an incorrect statement.
I was being redundant as "equal" can mean more than one thing.

I just thought of something else.

I just realized that infinite sets are dynamic. They are open ended. What I mean is that the process of placing elements into an infinite set never ends.

Therefore, infinite sets are never created. For something to be created, the creation process must end. God could not have been created. He is a set open ended at both ends. Eternal.

It's no wonder then that He refers to Himself as "I AM" the infinite set G is constantly growing, it had no beginning, and will have no end. It just is.
--> @Deb-8-a-bull
Trying to believe in this trinity sure does look painful.
As school must have been for you.

But lucky for you, you live in a country with a safety net for "special" people like you.

It isn't painful at all Deb, it just looks that way from your "special" vantage point.
--> @ethang5

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ethang5,

First thing, when I saw that you actually posted a new thread from your lengthy Satanic dry spell, I could not believe my eyes!!!  I had to turn off and on my computer many times to make sure it was true!

Now, unlike you, when you tip-toe into my threads and DO NOT discuss the topic at hand, but only to run away from it ad infinitum, I will address your topic within this break through thread of yours, praise Jesus!

I could almost hear your back break as you bent over backwards to try and prove that our ever loving and forgiving serial killer Jesus can be proved by higher math. Your dissertation sickens Jesus and I because the SIMPLE MATH is the fact that you only need FAITH to accept Jesus' existence in a Triune proposition, therefore once again, Jesus and  I have shown your outright biblical ignorance for the umpteenth time!

"And without faith it is impossible to please him, for whoever would draw near to God must believe that he exists and that he rewards those who seek him." (Hebrews 11:6)

Ethang5, what's next? Tarot cards?

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