The Well-Ordering Principle and (the theorem of) Mathematical In-duction (continued).This result is fascinating: it says mathematical induction, so useful as it is,depends only on a seemingly extremely weak axiom about the natural numbers:that every nonempty subset of the natural numbers contains a least element.Who wouldn't believe that?!In fact, we may prove the famous fundamental theorem of aritmetic (F.T.A.),i.e. that every integer admits an essentially unique factorization into primesusing only the seemingly meek W.O.P., and from the F.T.A. may we prove thesquare root of 2 ain't in Q.

The above question refers to the relationship between the Well-Ordering Principle (WOP) and the…

The Well-Ordering Principle and (the theorem of) Mathematical In- duction (continued). This result is fascinating: it says mathematical induction, so useful as it is, depends only on a seemingly extremely weak axiom about the natural numbers: that every nonempty subset of the natural numbers contains least element. Who wouldn't believe that?! In fact, we may prove the famous fundamental theorem of aritmetic (F.T.A.), i.e. that every integer admits an essentially unique factorization into primes using only the seemingly meek W.O.P., and from the F.T.A. may we prove the square root of 2 ain't in Q.

The Well-Ordering Principle and (the theorem of) Mathematical In- duction (continued). This result is fascinating: it says mathematical induction, so useful as it is, depends only on a seemingly extremely weak axiom about the natural numbers: that every nonempty subset of the natural numbers contains least element. Who wouldn't believe that?! In fact, we may prove the famous fundamental theorem of aritmetic (F.T.A.), i.e. that every integer admits an essentially unique factorization into primes using only the seemingly meek W.O.P., and from the F.T.A. may we prove the square root of 2 ain't in Q.

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Question

The Well-Ordering Principle and (the theorem of) Mathematical In-
duction (continued).
This result is fascinating: it says mathematical induction, so useful as it is,
depends only on a seemingly extremely weak axiom about the natural numbers:
that every nonempty subset of the natural numbers contains a least element.
Who wouldn't believe that?!
In fact, we may prove the famous fundamental theorem of aritmetic (F.T.A.),
i.e. that every integer admits an essentially unique factorization into primes
using only the seemingly meek W.O.P., and from the F.T.A. may we prove the
square root of 2 ain't in Q.

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