> For the complete documentation index, see [llms.txt](https://mandober.gitbook.io/math-debrief/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://mandober.gitbook.io/math-debrief/501-number-theory/terms/number1.md). # Number A **number** is a *mathematical primitive*, a concept that is not defined in terms of the previously defined concepts. Numbers, like all things in mathematics, lack physical form and only exist in the mind. Even there, a number lacks a more concrete manifestation, staying hidden underneath its symbolic representation. We rely on our intuition to understand the concept of a number apart from its numeric representation, but we use one of its representations (symbol, word, sign, gesture) to refer to it. In terms of sets (set is also a mathematical primitive), a number is a property that sets with the same number of elements share. The number zero is represented by the empty set; the number three is represented by sets that contain exactly three elements. Under a different set theory, the number three is the set that contains all other sets that have three elements. In terms of functions, in *Lambda Calculus*, numbers are represented through function application: the number of times a function is applied to its argument represents a certain number (so zero means a function is not applied at all, one means a function is applied once, two twice, and so on). numerals are strings of digits used to indicate magnitude. They measure size - how big or small a quantity is. the counting numbers are used to enumerate (count) the objects. scalars are numbers that are used to measure size, or how big or small something is. They represent the magnitude of a quantity. --- # Agent Instructions This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com. ## Querying This Documentation If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question. Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter: ``` GET https://mandober.gitbook.io/math-debrief/501-number-theory/terms/number1.md?ask=&goal= ``` `ask` is the immediate question: it should be specific, self-contained, and written in natural language. `goal` is optional and describes the broader end goal you are ultimately trying to accomplish on behalf of the user. GitBook uses it to tailor the answer towards what is most useful for that goal. The response will contain a direct answer to the question and relevant excerpts and sources from the documentation. Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.