I recall reading about a rule for multiplying ordinals where at least one is infinite, and where the cardinality of the multiplier (on right) is larger than the multiplicand (on left).
If I recall correctly it says that the result is the MAX of the two.
For example: $\omega * \omega ^2 = \omega^2$
However, I also recall reading that there are some exception cases wherein you can't just take the MAX. Am I remembering correctly... and if so, could I ask one of you nice folks for an example? Thanks in advance! -chris
In ordinal arithmetic $w(w+1)=w^2+w>w+1$ . Also $(w_1)*(w_1+w)=(w_1)^2 + w_1w>w_1+w$.