Perfection: A Mathematical Proof

Is perfection possible? Jesus commanded us to be perfect like God, our Father in Heaven. This page gives mathematical proof that it IS possible.


In mathematics, a “proof” is a series of statements such that:

  • the first statement of the series is accepted by everyone;
  • each new statement in the series is a logical consequence of
  1. the preceding statement in the series; and
  2. an additional statement that is also accepted by everyone; and
  • the series yields a useful result (the “conclusion”).

Mathematical proofs are made to put a permanent end to a question. A correct mathematical proof is beyond further debate; its conclusion must simply be accepted as fact.

This mathematical proof regarding perfection will provide such an answer to a long-standing question: "Is Perfection Possible?"


(Note: in mathematics, a statement that is accepted by everyone is called an “axiom”. I mention this for the sake of completeness; but I will not bother with using the word “axiom” further here.)

To make this proof, I need a clear statement of what it means to say someone is “perfect”. As we saw in “What Is Perfection?”, being “perfect” is “being without sin”.

In mathematical terms, this means

Perfect = being without sin.

It is also true that “forgiven” is “being without sin”. This is how King David began a prayer to God for forgiveness in Psalm 51:

Psalm 51:1-2

“1a Grace me, Elohim [God]! According to your kindness, according to the abundance of your compassion, wipe out my transgressions!

2 Wash my immense depravity from me, and cleanse me from my sin!”

In this prayer, we see that “forgiveness” is considered the same as having transgressions “wipe[d] out”. In Psalm 103:12, David says those transgressions are taken away from us “as far as the east is from the west”. In Micah 7:19, the prophet Micah says that forgiven sins will be sent “to the bottom of the sea”.

So, when sins are forgiven, they are GONE: the forgiven person is WITHOUT sin.

In mathematical terms, this means

Forgiven = being without sin.

The transitive property of mathematics tells us that

If a=b, and b=c, then a=c.

So, since

  • forgiven = being without sin; and
  • being without sin = perfect; we have
  • forgiven = perfect.

Another important point to note is that, when our sins are forgiven by God, and taken away from us, we are able to resist sin for some NON-ZERO amount of time. If this was NOT true, it would LOGICALLY mean that God’s forgiveness would free us from sin for ZERO amount of time: that is, God’s forgiveness would NOT free us from sin for ANY amount of time, regardless of how small. However, as we read in 1 Corinthians 10:13, God DOES “mak[e] together the test AND the escape”.

1 Corinthians 10:13

“13 You will not have gotten a test if an unbelieving person; but God, He will not be leaving you to be tested beyond what you are able, but will be making together the test and the escape, that you be empowered to endure.”

Since forgiven=perfect, this means that:

When we become perfect, we are able to resist sin, at least momentarily. Without loss of generality, let us assume that this resistance to sin lasts for at least one second.

(Note: if we ask God for forgiveness before going to sleep, we will likely be able to easily resist sin for considerably longer than a second, e.g., for the entire time we are asleep; but for the purposes of this proof, it is enough to assume we are able to resist sin for a very brief amount of time, such as a second.)

Also, it is accepted that:

A person who asks God for forgiveness will be forgiven.

Here is some Biblical evidence of this:

1 John 1:9

“9 If we confess our sins, He [God] is faithful and just, so that He forgives us those sins and cleanses us from every injustice.”

As Jesus said, “Ask, and it will be given to you” (Matthew 7:7; Luke 11:9).

We are now ready to begin the proof.


Theorem: Perfection is possible for any person.

Proof (by mathematical induction):


  • Suppose a person prays to God and asks for forgiveness.
  • This person is forgiven since we know that anyone who asks for forgiveness is forgiven.
  • This person is perfect since forgiven = perfect.
  • This person can remain perfect for at least one second since a perfect person can resist sin for some non-zero amount of time; and without loss of generality, we may assume the amount of time is one (1) second. This second will be t=1.

Thus, the person can be perfect for t=1 second.

t=i implies t=i+1:

  • Suppose a person is perfect for t=i number of seconds.
  • This person can remain perfect for at least one second since a perfect person can resist sin for some non-zero amount of time; and without loss of generality, we may assume the amount of time is one (1) second. This second will be t=i+1.

Thus, the person being perfect for t=i number of seconds implies the person can be perfect for t=i+1 number of seconds.

Q.E.D. (“Quod Es Demonstradum”, which is Latin for “it is demonstrated”; that is, “it is proven”)

This is all that is necessary to prove with mathematical certainty that it IS possible for a person to live perfectly.

What this mathematical proof basically shows is that, once we are forgiven, we can have perfection for as many seconds as we can resist sinning. If we just resist sin one second at a time, those seconds can add up into minutes, and hours, and days, and years of perfection.

This is a possibility: We can remain in this perfection. It does NOT say if we will remain in this perfection. How long we live in this perfection is our choice: it depends on whether or not we choose to sin.

UPDATE (November, 2014):

On February 14th, 2014, Michael Rood from ARoodAwakening.TV, while hosting the weekly Internet TV program "Shabbat Night Live", answered a question from one of the program's viewers.

The question was:

"How do we differentiate between keeping Torah in the [Holy] Spirit and legalism?"

At about 3 minutes and 45 seconds into the discussion of this question, Michael asks his guest, Chaim Goldman:

"Can you go, uh, 5 minutes without sinning?"

Chaim says he thinks that he can. Then Michael asks:

"Can you go 10 minutes?"

Chaim says he tries. Then Michael asks:

"Alright. So, at what point do you have to sin?"
(which is to say "When are you forced to sin?")

This is exactly the way of thinking about sin that is formally presented in the mathematical proof on this page!

If you would like to see this discussion, click this link:

(This page will open in a new window.)

The entire video (it's only 5 minutes and 14 seconds long) is embedded below.

(Note: in this over 5 minute long video, you will not see Chaim (or Michael) choosing to sin. So we also appear to have empirical evidence that Chaim (and Michael, too) can, indeed, "...go... ...5 minutes without sinning", in answer to that first question of Michael to Chaim.)

What this page makes obvious is that our choices regarding sin are real choices: we are NOT forced to choose to sin. When criticizers begin to criticize a person, it is common for them to say that the person chose to sin--chose not to use the “escape” provided by God. However, when the criticizers own sins become known, these criticizers claim that sin is INescapable.

Many, many people ignore the truth of God, and cling to the lie that we are forced to choose to sin. A choice can NEVER be forced on someone, because if something is forced, it is NOT a choice! People are not so stupid that they are unaware of this fact; rather, they ignore the truth.

Note that this is a type of sinless perfection: free from sins that are chosen. These are more commonly known by the names "willful sins" and "intentional sins". However, unlike Jesus, we are not able to be sinless in every way. We cannot avoid those sins known by the names "accidental sins" and "unintentional sins" (this type of sinning is referred to as "stumbling" in James 3:1-2).

Thus, it is possible for us to live in a type of sinless perfection; but in this present time, only Jesus is sinless in every way.

I close this page with a Biblical warning, to anyone considering rejecting the now proven reasoning of this page.

Romans 1:28

“28 And just as they prove to be unclinging towards God in knowledge, God gives them up to a disproven reasoning, to be doing the unbecoming.”


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