Introduction to Mathematics

N. Whitehead A.

Description

Whilst the greatest effort has been made to ensure the quality of this text, due to the historical nature of this content, in some rare cases there may be minor issues with legibility.

Sujets

• Sciences et techniques
• Calculus

Informations

• Publié par: Forgotten Books
• Date de parution: 27 novembre 2019
• Nombre de lectures: 0
• EAN13: 9780243758241
• Langue: English
• Poids de l'ouvrage: 4 Mo

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CH AP TER I A B S T A C T AT E AT H E AT C study of mathematics is apt to com mence in disappointment The important applications of the science the theoretic l interest of its ideas and the logical rigour of its metho s all generate the expectation of a speedy introduction to processes of interest We are told that by its aid the stars are weighed and the billions of molecul s in a drop of water are counted like the ghost of Hamlet s father this great science eludes the efforts of our ment l weapons to grasp here tis there tis gone and what we do see does not suggest the same excuse for illusiveness as sufficed for the ghost that it is too noble for our gross methods show of violence ever excusable may s rely be offered to the trivial results which occupy the

I TRODUCTION M A THEM A TICS pages of some elementar y mathematic l treatises The reason for this failure of the science to live up to its reputation is that its funda mental ideas are e l ine to student disentangled rom the technical p ocedure which has be invente to fa ilitate their exact presentation in particular inst nces ccordingly the unfortunate learnerfinds himself str ggling to acqu re a knowledge of a mass of details which are not illuminated by any general conception Without a doubt technical facility is afirst requisite for alu ble mental activity we shall fail to ciate the rhythm of ilton or the passion of S helley so long as wefind it necessary to spell the words and are not quite certain of the forms the individual letters In this sense t ere is no roy l road to it is equally an error to cofine attention to technical processes excluding consideration of general ideas Here l ies the ro d to pedantry T the following e t hapters is nothe obj to teach mathematics but to enable stude t from very b egin ing of thei co rse to know what the science is ab ut and why it is neces arily the foundation of exact thought as pplied to natural phenomena allu sion in what follows to det iled deductio in part of the science w ll be inser e

A URE O F M A THE A TICS merely for the purpo e of example and care l taken to make the general ar ume t comprehensible even if here and there some technical process or s y mbol which the reader does not understand is cited for the purpose illustration Thefirst acquaint nce which most p ople have with mathematics is through arithmetic hat two and make four is usually taken as the t pe of a simple mathematical pro pos tion which everyone will have heard of ithmetic therefore w ll be a good subj ec to consider in order to discover if possible the most obvious characteristic of the science Now thefirst noti about arithmeticeable fact that it applies to everything to tastes and sounds to apples and to angels to the id as of the mind and to the bones of the bod y T he nature of the things is perfectly i di ferent of things it is true that two and two make four T we write down as lead g charac eristic of mathematics th t it deals w th properties and which are applicable to things j ust becau e they are things and apart from any pa ticular eelin s or emotions or sensations in any way co e ted with them T is is what meant b y call ing mathematics an abstract T deservec ed he result whi h we have e t e tio It nat ral to hin that