There are many different numeral systems, that is, writing systems for expressing numbers.
"A base is a natural number B whose powers (B multiplied by itself some number of times) are specially designated within a numerical system." The term is not equivalent to radix, as it applies to all numerical notation systems (not just positional ones with a radix) and most systems of spoken numbers. Some systems have two bases, a smaller (subbase) and a larger (base); an example is Roman numerals, which are organized by fives (V=5, L=50, D=500, the subbase) and tens (X=10, C=100, M=1,000, the base).
Numeral systems are classified here as to whether they use positional notation (also known as place-value notation), and further categorized by radix or base.
The common names are derived somewhat arbitrarily from a mix of Latin and Greek, in some cases including roots from both languages within a single name. There have been some proposals for standardisation.
All known numeral systems developed before the Babylonian numerals are non-positional, as are many developed later, such as the Roman numerals. The French Cistercian monks created their own numeral system.