- In mathematics, the natural numbers are the numbers 1, 2, 3, etc., possibly including 0 as well. Some definitions, including the standard ISO 80000-2, begin the natural numbers with 0, corresponding to the non-negative integers 0, 1, 2, 3, …, whereas others start with 1, corresponding to the positive integers 1, 2, 3, … Texts that exclude zero from the natural numbers sometimes refer to the natural numbers together with zero as the whole numbers, while in other writings, that term is used instead for the integers (including negative integers). In common language, particularly in primary school education, natural numbers may be called counting numbers to intuitively exclude the negative integers and zero, and also to contrast the discreteness of counting to the continuity of measurement—a hallmark characteristic of real numbers.
- Infinity (plato.standford.edu)
Infinity is a big topic. Most people have some conception of things that have no bound, no boundary, no limit, no end. The rigorous study of infinity began in mathematics and philosophy, but the engagement with infinity traverses the history of cosmology, astronomy, physics, and theology. In the natural and social sciences, the infinite sometimes appears as a consequence of our theories themselves (Barrow 2006, Luminet and Lachièze-Rey 2005) or in the modelling of the relevant phenomena (Fletcher et al. 2019). Mathematics itself has appealed to some form of infinity from its beginning (infinitely many numbers, shapes, iterated addition or division of segments) and its contemporary practice requires infinitary foundations. Any field that employs mathematics at least flirts with infinity indirectly, and in many cases courts it directly.