The Goldbach conjecture

[John Yeadon]

One form of the Goldbach conjecture has it that 'every even number
greater than two can be written as the sum of two primes'.
Equations such as Pythagoras and pi R squared work and make sense even
if one of the dimensions is infinite. But does that work on the
Goldbach conjecture? I argue that the Goldbach conjecture falls down
because it just does not work with infinities. Is there such a thing as
an even infinity and is there an infinite prime?

It probably works for all finite even numbers - nobody has found an even
number it doesn't work for - (yet). But it just does not make sense
with infinities and it has to work with infinities to work fully. You
cannot make it work by making an exception for infinity, or can you?

[Frank J. Lhota]

Goldback was only conjecturing about the natural numbers, i.e. the
non-negative finite integers. It clearly does not work for infinite
cardinals. If n is an infinite cardinal, then n = 2*n, so all infinite
cardinals are even. On the other hand, no infinite cardinal is a prime
in the customary sense of the term.

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