Download Applied Numerical Analysis - Solutions manual by Curtis F. Gerald Patrick O. Wheatley PDF

By Curtis F. Gerald Patrick O. Wheatley

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S 3, We have been speaking of two points linked by five conductors. However, we can manage with only one conductor by transmitting each letter as a succession of five binarY,pigits (impulse or no impulse). :. \ • 26,r' The Binary Systcm-A Guardian of Secrets . 1Jseful application of the binary system in telegraphy. • 11. The Binary S)'Stem-:-A GurdiaD of Secrets Telegraph and. fast transfer of information. , especially in military matters, i~fonnatiQn must be made accessible \only to the intended recipient of message.

020202... actually signifies the sum of the geometric progression w~ich, by the formula, is equal to 2/9 1 - 1/9 2/9 = 8/9 = 1/4. By using the following geometric argument, we can persuade our~ selves that the point t 14 will not be deleted. The point 1/4 divides the whole interval [0, I] in a ratio of I : 3. After the removal of the segment [1/3. 2/3}, the point 1/4 remains in the half~open interval [0,1/3), which it divides in a ratio of 3: 1. open interval (2/9. 113), which it divides in a ratio of 3:·1, and so on.

On Infinite Numlwr hpresenlalions of the partial segments which it bounds. In other words, we can eliminate either all fractions cOnsisting of" infinitely 'repeating" zeros, or fractions consisting of .. infinitely repea . ng" nines. If we intrOduce such a restriction. \lch point of the lint by a unique infinite'decimal ansion. , That we h~ve successively . oed the partial segments into 10 parts is, of covrse, immaterial. In,~te d of 10, we could have used some other number, say 2, div4ding each partial segment in half.