> This way, you could create any two "dimensionless" quantities and try to compare them or use one in place of the other which might be meaningless.
replyCase in point:
Yeah, "dimensionless" would mean they have equal dimension, which would mean they are comparable, which isn't necessarily the case. E.g. both radians and degrees are called "dimensionless".
replyEdit: Apparently "same dimension" doesn't imply "same unit".