...but a new record cold or warm temperature will never, ever occur in this range again....
Why not?
Just in case you were mistaken, this is for a specific climate station, not the whole world (I don't think I made that clear
)
So, say for example the highest record low ever recorded for a location is 57°.
Record low = coldest ever for a specific day.
A record low can not ever be higher than 57°, because that just so happens to be the highest temperature that is still considered a record low for a specific day.
Record high = warmest ever for a specific day
If the lowest record high recorded for the same station is 66°, there can never be a record high cooler than that temperature, it is absolutely impossible (unless said record is deemed unofficial for some reason).
Using this example: 62° will NEVER, EVER be recorded as a RECORD HIGH OR LOW, because it is too warm to be considered a record low (highest record low is 57°), but too cool to be a record high (lowest record high is 66°) for any day in the year.
62° could be a RECORD LOW HIGH or RECORD HIGH LOW, which essentially means that there has never been a cooler high or warmer low in that stations history, but it is not the same as the coldest low or warmest high.
Hopefully this made more sense.