Current varieties of English find one set of numbers sufficient. I exclude binary on the pirnciple that it is not used for counting except as a geeky in-joke. I must specify current English because there were rural systems of counting, in formerly Welsh areas such as Cumbria; the non-English system was restricted to counting herd animals, a limited but very important semantic domain for the local culture. In Korean, and I believe Japanese also, there are two counting systems: one native, and one adopted and adapted from the Chinese spoken at the time of contact. A comparison that might make more sense to those who only know Indo-European languages: this situation is as if Slavic-speakers counted numbers using Slavic numerals, but counted things using Greek.
I can more readily recognize the Sino-Korean numbers, thanks to the small amount of Chinese I learned (sadly, the lack of oral practice has made the tones nigh-impossible). Most of the numbers are easily recognizable, although I did briefly find the Sino-Korean vs. native Korean distracting. The use of Sino-Korean numerals as count nouns accords with the isolating, SVO, head-final nature of Chinese, while the agglutinative, SOV, head-final structure of Korean precludes count nouns except as a borrowing from culture languages of the area (i.e., Chinese). The head-final feature of Korean, however, does provide a convenient location for the count noun. The optionality of the plural suffix - a not uncommon feature of non-Indo-European languages - in Korean also makes the count nouns welcome.
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