Omega is the lowest countable infinity. There's no parity within a countable infinite as you describe.
It's only even or odd with respect to other infinities which the cardinal numbers can count based on the presence of a bijection or not. It's a kind of relative parity.
> There's no parity within a countable infinite as you describe.
That directly contradicts the quoted text I included from the original answer though, as far as I understand. It directly asserted that "every infinite cardinal is even".
> It's a kind of relative parity.
What is relative parity? The original question was whether infinity is even or odd... I don't know what you mean by relative parity.
It's only even or odd with respect to other infinities which the cardinal numbers can count based on the presence of a bijection or not. It's a kind of relative parity.