The symbols “11” mean eleven, three, or two by base
A numeral system writes numbers without words—positional digits or sign-value marks in a fixed scheme. The string 11 is eleven in base ten, three in binary, and two in unary. Roman, Greek, and Egyptian numerals famously lack a standard zero glyph.
Good systems represent a useful set such as integers or rationals, give each value a unique or at least standard writing, and mirror arithmetic structure so calculation stays manageable. Ordinary decimal notation gives every nonzero natural number exactly one finite digit string that starts with a nonzero digit. The phrase number system is best avoided here, since it can also mean the real, complex or p-adic numbers themselves.
Early civilizations went their own ways: Babylonians counted in sixties, Egyptians wrote hieroglyphic numerals, and the Chinese used rod numerals. Needs such as accounting, trade, taxes, astronomy and land surveying drove the designs. Many early schemes repeated symbols or combined signs for units and higher powers, whereas positional systems let a symbol's worth depend on where it stands, so big numbers need few marks. A placeholder, and later a true zero, made written calculation far more systematic.
The Maya independently built a base-20 system with its own zero symbol. In India, Brahmagupta in the seventh century set out rules for calculating with zero, later refined by al-Khwarizmi. The Hindu–Arabic system, the first true written positional notation, existed in India by the seventh century, though dots or blank spaces often stood in for zero; the first widely accepted zero dates to 876.
Fibonacci used Western Arabic numerals in his Liber Abaci, and by the thirteenth century European mathematicians accepted them despite early resistance, prized for banking and trade. Printing in the fifteenth century helped them displace Roman numerals, by the seventeenth they ruled scientific work from Newton to Descartes, and by the late twentieth century almost every calculation done without a computer used them.
Source: Numeral system
