Full Idea
Unlike the transfinite cardinals, the transfinite ordinals do not obey the commutative law, and their arithmetic is therefore quite different from elementary arithmetic.
Clarification
'Commutativity' is to still work if you change the order of the terms
Gist of Idea
Transfinite ordinals don't obey commutativity, so their arithmetic is quite different from basic arithmetic
Source
Bertrand Russell (The Principles of Mathematics [1903], §290)
Book Reference
Russell,Bertrand: 'Principles of Mathematics' [Routledge 1992], p.312