The reason the nine numbers after ten are known as eleven, twelve, and the teens is clarified by looking at Roman numerals.
In other words, they are all plus or minus units of ten and were interpreted into archaic English with this in mind.
Eleven (XI) or “leave one” means ten is one less than eleven.
Twelve (XII) means ten is two less than twelve.
Thirteen is three plus ten (or “teen”), four plus ten is fourteen, and so on.
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