Theory of elementary sets: for two ordinals, $ | A | nleq | B | $, Can you conclude $ | A |> | B | $?

For two ordinals, $ | A | nleq | B | $, we can conclude? $ | A |> | B | $?

Observe the $ <$ Here they represent the cardinal order.

I was thinking of using the linear order relationship of $ A $ Y $ B $ in ordinal, but I'm not sure if it's possible without the AC discussion.