I once developed a shortcut notation to simplify reasoning about ranges differentiating between "point cero" and "interval between 0 to 1", to make off-by-one errors less likely, but in the end it was functionally equivalent to the popular open/closed interval notations.

   /9..10\  : "short" interval : size 1 (hour)  ==  half-open interval [9..10)
 -|20..21|- :  "long" interval : size 2 (days)  ==  closed interval   [20..21]

Ultimately, it relies on conventions, but I guess now you can see how this one relies on something which has some consistent pattern.

English in general makes this distinction: "He is fewer than 6 years old" is simply a mistake, while "less than 6 years old" is fine. (I think some dialects use "fewer" less often, in general, but would be pretty surprised if any prefer it here.)

Other languages use a less confusing term for it: anniversaire (French) is just anniversary, verjaardag (Dutch) roughly means year-rollover-day, and cumpleaños (Spanish) signifies completion of another year.

late 14c., from Old English byrddæg, "anniversary or celebration of one's birth" (at first usually a king or saint); see birth (n.) + day. Meaning "day on which one is born" is from 1570s. Birthnight is attested from 1620s. https://www.etymonline.com/word/birthday#etymonline_v_27158

I know there are studies on how birth date affects future success in school (though IIRC I read in Gladwell, and I'm wary of accurate his read on things are), I wonder if that effect is compounded with this system?

Americans do this a lot too, except at a (pseudo) decade level, e.g. "are you a '90s kid?"

This brings up other ambiguities. A "90's kid" might have been born in the 80's.

You could say that the American school year is 0-based. Except instead of naming it zeroth grade, it is named kindergarten.

those are the same number.