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The Positive Integers are Well Ordered
Most likely, you answered the questions posed in with an enthusiastic yes, in part because you wanted the shot at the money, but more concretely because it seems so natural.
The Positive Integers are Well Ordered
Most likely, you answered the questions posed in with an enthusiastic yes, in part because you wanted the shot at the money, but more concretely because it seems so natural. But you may be surprised to learn that this is really a much more complex subject than you might think at first. In , we discuss the development of the number systems starting from the Peano Postulates. Although we will not devote much space in this chapter to this topic, it is important to know that the positive integers come with some assembly required. In particular, the basic operations of addition and multiplication don't come for free; instead they have to be defined.
As a by-product of this development, we get the following fundamentally important property of the set \(\posints\) of positive integers:
An immediate consequence of the well ordered property is that the professor will indeed have to pay someone a dollareven if there are infinitely many students in the class.
Ngayon ikaw Walang kalkulador settles ito isa, ngunit ang mga piraso ng mga ito ay computable. Subukan ang isa sa ibaba, o type ang iyong sarili.
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Mga katanungan na tanong ng mga tao
Permutation or combination?
Ask whether order matters. A lock code is a permutation (order matters); a hand of cards is a combination (it does not).
What is a graph in this sense?
Dots (vertices) joined by lines (edges), not a plot. Road maps, social networks and molecules are graphs; questions like "is there a route" and "how few colours" are graph theory.
Bahagi ng pahinang ito ay naaayon mula sa Keller & Trotter, Applied Combinatorics (CC BY-SA 4.0). Condensed at muling ipinaliwanag dito; errors ay aming.
Higit pa sa Combinatorics & Graph Theory
The counting principlesPigeonhole principle and inclusion, exclusionBinomial coefficients and Pascal's triangleRecurrences and generating functionsGraphs: vertices, edges, degreesPaths, cycles, trees, Euler and HamiltonColouring and planar graphs