More even than odd

I was amazed this morning to discover a "proof"¹ for something that is quite counter-intuitive. I mean, there are as many odd numbers as even numbers, right?
    Wrong. There are actually more even numbers than odd numbers. Here's the proof that came to me while I was eating my grapefruit half:
    If you add an even number of even numbers, you get an even number.
    But you also get an even number if you add an even number of odd numbers! And you don't conversely get any extra odd numbers when you add an odd number of even numbers. Rather, you seem to gain some even numbers—or lose some odd numbers, depending on how you look at.
    Therefore, there are apparently more even numbers than odd ones. And I haven't even tried to find other ways we might gain even numbers or lose odd ones.
    Isn't that amazing!

How can that be? Can that possibly be right?
    If true, it is so astounding, do you think maybe this might be a clue toward discovering a proof for the existence of God? Or maybe for the existence of two of them (God even rather than odd)? Or for their nonexistence? Wow.
    What if duotheism is the True Way, rather than monotheism? Or if atheists have to deny the existence of two Gods in order to be atheists? "Aduotheists" is hard to pronounce.

An odd God limerick

More even than odd...the truth about God?
Then let's swell the ranks of Their Squad,
    Double Their pronouns,
    Use King and Queen crowns,
And on Fridays eat twice as much cod.

Notes for further analysis:

1. The operator "even number of" is equivalent to "multiplied by two" (or "the numerical result made even").
2. The operator "odd number of" is not equivalent to "the numerical result made odd" (if the things there are an odd number of are even numbers).

    Further disquisition
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1. Note: This post is labeled "humor." I only added this note later when I suspected that some readers had not detected the post's parody of wishful or theological thinking, possibly because they'd noticed that I'd lately been taking myself so very seriously.