But the first part is called prefix even in the standard itself. I wanted to make that distinction because it's not important what the base unit is. By speaking about prefixes instead of the unit as a whole I wanted to make it clear that you can (at least in theory) use any base unit. So everything I said about KiB and kB is also true for Kib and kb and even for kK (kilokelvin) and KiB (kibikelvin) 🤣
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