I considered deleting the post, but this seems more cowardly than just admitting I was wrong. But TIL something!
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∞ = ∞ x 2
That's not a true statement. 2∞ < ∞ and ∞ < 2∞ is how you'd write it.
Otherwise you could subtract infinity from both sides and get 0 = ∞.
Except subtraction is not applicable in this case
Not true. 2∞ is not bigger or smaller than ∞. This is explained by Hilbert's hotel. And subtracting infinity from infinity is undefined so you do not get 0 = ∞.
even if that's not how you can write it, one gets the same issue in yours subtracting infinity from both sides