User blog comment:Vel!/On salad numbers/@comment-5150073-20120912091904/@comment-80.98.179.160-20171113171316

\(2\omega\ne\omega\)

Because then ω must be 0, else 2ω would NEVER be equal to ω. (But ω is transfinite, and no transfinite is 0)

Multiply 2 by any ordinal, you'll ONLY get the same ordinal if it's 0!

Similarly, 1+ω>ω due to the Axioms being violated if 1+ω=ω!