Leading exponent of an ordinal product
= Leading exponent of an ordinal product
Let nonzero ordinals $\xi,\eta$ have leading exponents $\rho,\sigma$. If $\eta$ is finite, then $\xi\eta$ has leading exponent $\rho$. If $\eta$ is infinite, so that $\sigma>0$, then $\xi\eta$ has leading exponent $\rho+\sigma$. This follows by multiplying the leading terms in <Cantor normal form> and using continuity of <ordinal multiplication> at limit ordinals.