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