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Note, your original set wasn't "equally spaced" as the ω at the end is an infinite distance from the rest of the set,Wrong. The infinite distance between 0 and ω is realized by only natural numbers. Note that there are infinitely many natural numbers and not the least space between them and ω.
so you can't use equal spacing logic on the second set.ω is amidst the interval (0, ω2) because in the image there are as many ordinals in (ω, ω2) as in (0, ω).
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