If there exists a single (even whole number greater than 2) that
cannot possibly be proved to meet the Goldbach criteria then the
Goldbach conjecture is not true.

A is the set of (even whole numbers greater than 2)
P means {Provably meet the Goldbach criteria}
x ∈ (even whole numbers greater than 2)

This proof is defined as the sequence of steps required to verify that x
is the sum of two primes.

¬Goldbach ⇔ ∃x ∈ A, ¬P(x) // first paragraph translated into math

Math correctly transforms it into this
Goldbach ⇔ ∀x ∈ A, P(x)

⇔ if and only if;
https://en.wikipedia.org/wiki/List_of_logic_symbols

Goldbach if and only if
all elements of the set of
(even whole numbers greater than 2)
Provably meet the Goldbach criteria

If it is impossible to prove that any element of the set of (even whole
numbers greater than 2) does not meet the Goldbach criteria then the
Goldbach conjecture is false translates into

Unless every element of the set of (even whole numbers greater than 2)
provably meets the Goldbach criteria then the Goldbach conjecture is false.

translates into
Unless the Goldbach conjecture is provable it is not true.

--
Copyright 2021 Pete Olcott

Talent hits a target no one else can hit;
Genius hits a target no one else can see.
Arthur Schopenhauer

On 3/7/22 10:58 AM, olcott wrote:
> If there exists a single (even whole number greater than 2) that
> cannot possibly be proved to meet the Goldbach criteria then the
> Goldbach conjecture is not true.
>
> A is the set of (even whole numbers greater than 2)
> P means {Provably meet the Goldbach criteria}
> x ∈ (even whole numbers greater than 2)
>
> This proof is defined as the sequence of steps required to verify that x
> is the sum of two primes.
>
> ¬Goldbach ⇔ ∃x ∈ A, ¬P(x) // first paragraph translated into math
>
> Math correctly transforms it into this
> Goldbach ⇔ ∀x ∈ A, P(x)
>
> ⇔ if and only if;
> https://en.wikipedia.org/wiki/List_of_logic_symbols
>
> Goldbach if and only if
> all elements of the set of
> (even whole numbers greater than 2)
> Provably meet the Goldbach criteria
>
> If it is impossible to prove that any element of the set of (even whole
> numbers greater than 2) does not meet the Goldbach criteria then the
> Goldbach conjecture is false translates into

And how do you PROVE that it is impossible to prove that any element of
that set doesn't meet the Goldbach criteria?

>
> Unless every element of the set of (even whole numbers greater than 2)
> provably meets the Goldbach criteria then the Goldbach conjecture is false.
>
> translates into
> Unless the Goldbach conjecture is provable it is not true.

Nope. FAIL.

Having to prove an infinite number of propositions is NOT a proof.

You really have shown that you don't understand even the basics of Logic
101.

On 3/7/2022 6:00 PM, Richard Damon wrote:
> On 3/7/22 10:58 AM, olcott wrote:
>> If there exists a single (even whole number greater than 2) that
>> cannot possibly be proved to meet the Goldbach criteria then the
>> Goldbach conjecture is not true.
>>
>> A is the set of (even whole numbers greater than 2)
>> P means {Provably meet the Goldbach criteria}
>> x ∈ (even whole numbers greater than 2)
>>
>> This proof is defined as the sequence of steps required to verify that
>> x is the sum of two primes.
>>
>> ¬Goldbach ⇔ ∃x ∈ A, ¬P(x) // first paragraph translated into math
>>
>> Math correctly transforms it into this
>> Goldbach ⇔ ∀x ∈ A, P(x)
>>
>> ⇔ if and only if;
>> https://en.wikipedia.org/wiki/List_of_logic_symbols
>>
>> Goldbach if and only if
>> all elements of the set of
>> (even whole numbers greater than 2)
>> Provably meet the Goldbach criteria
>>
>> If it is impossible to prove that any element of the set of (even
>> whole numbers greater than 2) does not meet the Goldbach criteria then
>> the Goldbach conjecture is false translates into
>
> And how do you PROVE that it is impossible to prove that any element of
> that set doesn't meet the Goldbach criteria?

Every element (even integers > 2)
is either the sum of two primes or it is not.

Goldbach(N) ⇔
N ∈ (even integers > 2)
∃X ∈ prime_number
∃Y ∈ prime_number
| (X + Y = N)

>
>>
>> Unless every element of the set of (even whole numbers greater than 2)
>> provably meets the Goldbach criteria then the Goldbach conjecture is
>> false.
>>
>> translates into
>> Unless the Goldbach conjecture is provable it is not true.
>
> Nope. FAIL.
>
> Having to prove an infinite number of propositions is NOT a proof.
>

Goldbach(N) ⇔
N ∈ (even integers > 2)
∃X ∈ prime_number
∃Y ∈ prime_number
| (X + Y = N)

The sequence of steps required to confirm that N is the sum or two
primes is its proof that N has the Goldbach property.

https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence

If for any reason these steps cannot be performed or fail to confirm
that N is the sum of two primes then the Goldbach conjecture fails.

This logically entails that Goldbach is not true unless every N ∈ (even
integers > 2) is provable, thus true cannot exist apart from provable.

> You really have shown that you don't understand even the basics of Logic
> 101.
>
>
>

--
Copyright 2021 Pete Olcott

Talent hits a target no one else can hit;
Genius hits a target no one else can see.
Arthur Schopenhauer

On 3/8/22 12:20 PM, olcott wrote:
> On 3/7/2022 6:00 PM, Richard Damon wrote:
>> On 3/7/22 10:58 AM, olcott wrote:
>>> If there exists a single (even whole number greater than 2) that
>>> cannot possibly be proved to meet the Goldbach criteria then the
>>> Goldbach conjecture is not true.
>>>
>>> A is the set of (even whole numbers greater than 2)
>>> P means {Provably meet the Goldbach criteria}
>>> x ∈ (even whole numbers greater than 2)
>>>
>>> This proof is defined as the sequence of steps required to verify
>>> that x is the sum of two primes.
>>>
>>> ¬Goldbach ⇔ ∃x ∈ A, ¬P(x) // first paragraph translated into math
>>>
>>> Math correctly transforms it into this
>>> Goldbach ⇔ ∀x ∈ A, P(x)
>>>
>>> ⇔ if and only if;
>>> https://en.wikipedia.org/wiki/List_of_logic_symbols
>>>
>>> Goldbach if and only if
>>> all elements of the set of
>>> (even whole numbers greater than 2)
>>> Provably meet the Goldbach criteria
>>>
>>> If it is impossible to prove that any element of the set of (even
>>> whole numbers greater than 2) does not meet the Goldbach criteria
>>> then the Goldbach conjecture is false translates into
>>
>> And how do you PROVE that it is impossible to prove that any element
>> of that set doesn't meet the Goldbach criteria?
>
> Every element (even integers > 2)
> is either the sum of two primes or it is not.
>
> Goldbach(N) ⇔
> N ∈ (even integers > 2)
> ∃X ∈ prime_number
> ∃Y ∈ prime_number
> | (X + Y = N)
>
>>
>>>
>>> Unless every element of the set of (even whole numbers greater than
>>> 2) provably meets the Goldbach criteria then the Goldbach conjecture
>>> is false.
>>>
>>> translates into
>>> Unless the Goldbach conjecture is provable it is not true.
>>
>> Nope. FAIL.
>>
>> Having to prove an infinite number of propositions is NOT a proof.
>>
>
> Goldbach(N) ⇔
> N ∈ (even integers > 2)
> ∃X ∈ prime_number
> ∃Y ∈ prime_number
> | (X + Y = N)
>
> The sequence of steps required to confirm that N is the sum or two
> primes is its proof that N has the Goldbach property.

Right, you can prove that a FINITE number of N have the property.

>
> https://en.wikipedia.org/wiki/Curry%E2%80%93Howard_correspondence
>
> If for any reason these steps cannot be performed or fail to confirm
> that N is the sum of two primes then the Goldbach conjecture fails.

Except to prove the Goldbach conjecture, you need to prove this for an
INFINITE number of N, which can not be done in finite time, so it does
not form an Analytic Proof.

FAIL.

>
> This logically entails that Goldbach is not true unless every  N ∈ (even
> integers > 2) is provable, thus true cannot exist apart from provable.

Nope, you can't complete a finite proof if it needs an infinite number
of steps.

>> You really have shown that you don't understand even the basics of
>> Logic 101.
>>
>>
>>
>
>

Ultimatly, you are just showing that you don't even know the basic
definiton of what a 'Proof' actually is.

FAIL.