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
even if that's not how you can write it, one gets the same issue in yours subtracting infinity from both sides
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 = ∞.