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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.
Most te. Nincs számológép rendezi ezt, de a darabjai komposztálhatóak. Próbálja ki az egyiket lentebb, vagy gépelje be a sajátját.
Egy ingyenes fiók jegyzeteket ad minden leckéről, egy feljegyzést arról, hogy mit végeztél el, a megoldott problémáidról egy helyen, és egy oktatót, akit megkérdezhetsz erről az oldalról. A matematika maga mindenki számára nyitva áll, bejelentkezve vagy sem.
Regisztrálj! BejelentkezésItt használt szimbólumok
Koppintson a teljes definícióra, a képre és arra, hogy mit jelent minden betű.
Kérdések, amiket az emberek feltesznek
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.
Az oldal részei adaptálva Keller & Trotter, Applied Combinatorics (CC BY-SA 4.0). Össze van zavarodva és újra megmagyarázva; a hibák a miénk.
Még több 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