21. Understanding these patterns allows you to quickly calculate divisibility of seven as seen in the following examples: 22. As used in an empirical scientific theory, there is always a smallest as yet verified divisibility . 23. Things like primeness and divisibility don't change, although the representation of the numbers does. 24. As a simple example, the divisibility order on the natural numbers is an anti-symmetric relation. 25. For a 3-digit number in base 10, this number has a relatively simple divisibility test. 26. Infinite divisibility does not imply gap-less-ness : the rationals do not enjoy the uncountably infinite. 27. Eventually, one realises that the system is in some way " about " divisibility by three. 28. The concept can be generalized to sequences with values in any ring where the concept of divisibility is defined. 29. To see this, one first needs to introduce two concepts : the notion of divisibility for pairs of polynomials. 30. The definition extends to more general projective systems, such as those indexed by the positive integers ordered by divisibility .
