Fundamental Conceptions of Modern Mathematics volume 1
Fundamental Conceptions of Modern Mathematics volume 1
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In our eReader you can find the full English version of the book. Read Fundamental Conceptions of Modern Mathematics volume 1 Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Fundamental Conceptions of Modern Mathematics volume 1
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That the series of Algebra are variables is, one would think, sufficiently clear from the mere fact that nearly all the discussions of series in mathematical works bear upon their convergence or want of convergence that is, their tending or failure to tend to a limit. And yet it would be difficult to find anywhere an explicit statement to the effect that a series is a variable. Some definitions of "series" are indeed glaringly erroneous. Thus, in a comprehensive work of high repute by Professor... G. Chrystal, 1 we are told that " By a series is meant the sum of a number of terms formed according to some common law. ... An Arithmetic Series or an Arithmetic Progression, as it is often called, is a series in which each term exceeds the preceding by a fixed quantity. " That with the series to which mathematicians have paid most attention, summation plays an essential part, affords not the slightest excuse for defining a summative series as a sum; while there is lacking even the shadow of a pre- text to justify speaking of a sum whose summands con- stitute a progression as the progression itself.
What to read after Fundamental Conceptions of Modern Mathematics volume 1?
You can find similar books in the "Read Also" column, or choose other free books by Robert P Robert Porterfield Richardson to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
That the series of Algebra are variables is, one would think, sufficiently clear from the mere fact that nearly all the discussions of series in mathematical works bear upon their convergence or want of convergence that is, their tending or failure to tend to a limit. And yet it would be difficult to find anywhere an explicit statement to the effect that a series is a variable. Some definitions of "series" are indeed glaringly erroneous. Thus, in a comprehensive work of high repute by Professor... G. Chrystal, 1 we are told that " By a series is meant the sum of a number of terms formed according to some common law. ... An Arithmetic Series or an Arithmetic Progression, as it is often called, is a series in which each term exceeds the preceding by a fixed quantity. " That with the series to which mathematicians have paid most attention, summation plays an essential part, affords not the slightest excuse for defining a summative series as a sum; while there is lacking even the shadow of a pre- text to justify speaking of a sum whose summands con- stitute a progression as the progression itself.
What to read after Fundamental Conceptions of Modern Mathematics volume 1?
You can find similar books in the "Read Also" column, or choose other free books by Robert P Robert Porterfield Richardson to read onlineMoreLess
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