The Difference Between Number and Digit: From Semiotics to Mathematical Philosophy In everyday speech, the words "number" and "digit" are often used as synonyms, however, from a scientific, linguistic, and mathematical perspective, there is a fundamental and insurmountable difference between them. The confusion here is analogous to the mixing of the concepts of "letter" and "word". Understanding this difference is critically important for precise thinking in mathematics, informatics, linguistics, and philosophy. Semiotic Foundation: Sign and Meaning The key to distinguishing between them lies in the theory of signs (semiotics). Digit — this is a SIGN, SYMBOL. A specific graphic symbol used for recording numbers. This is a material object (a drawing on paper, a glow on the screen, a combination of signals in the processor), which indicates, encodes a certain quantitative value within the framework of a given numeral system. The Arabic digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are the ten basic digits of the decimal system. The Roman symbols I, V, X, L, C, D, M are digits of another, non-positional system. Number — this is an ABSTRACT ENTITY, IDEA, MEANING. This is a mental concept indicating quantity, magnitude, order, or code. The number "five" exists independently of how it is written: as a digit 5, a Roman numeral V, the word "five", five sticks |||||, a binary code 101, or as a collection of any five objects. Number is the meaning behind the digit. A simple analogy: Digit — this is an envelope with an address written on it. Number — this is the content of the letter, information. Different envelopes (digits of different systems) can carry the same letter (the same number). Mathematical and Historical Perspective History of development: Primitive people operated with numbers (the idea of "many" or "few", using notches, knots, pebbles), but did not have a developed system of digits. The creation of digits (as with the Sumerians, Egyptians, Maya) was a giant cultural leap ... Read more