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}
¬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

--
Copyright 2021 Pete Olcott

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

[ Followup-To: set ]

In sci.math olcott <NoOne@nowhere.com> wrote:

[ .... ]

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

No, you're wrong. You're as wrong as the people who believe the Earth
is flat. Both your belief and those of the flat-Earthers were
respectable things to believe in times past, but our knowledge of these
things has advanced in recent decades and centuries.

The Goldbach Conjecture is, of course, true if every large enough even
number is the sum of two primes, provably or not. Make sure you don't
venture too close to the edge of the Earth. ;-)

> --
> Copyright 2021 Pete Olcott

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

--
Alan Mackenzie (Nuremberg, Germany).