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Proceedings of the Edinburgh Mathematical Society Volume 16

Proceedings of the Edinburgh Mathematical Society Volume 16


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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1898 Excerpt: ...that number of arbitrary constants. In the case of equations of the first order, the critical locus has been analysed into cusp-locus, tac-locus, and envelope singular solution, and criteria for each have been given. No such analysis of the critical locus of an equation of, say, the second order has been attempted, and no criterion for the existence of singular solutions given. Still, it is possible that in a physical problem it might be well to bear in mind that, outside of the most general solution of an equation, solutions of a less degree of generality might also exist, and might be of a very different form. Seventh Meeting, June Qth, 1898. Dr Mackay in the Chair. Permutations: Alternative Proofs of Elementary Formulas. By R, F. Muirhead, M.A., B.Sc. 1. The number of the r-permutations of n things is the same as the number of ways of adding r things to a row which originally contains n-r other things. For suppose the n letters A, B, C... N to be placed in a row, then each permutation consisting of r letters may be indicated by placing below those r letters in the row, the digits 1, 2, 3... r, to indicate the order they have in the permutation. We may suppose zeros placed below all the remaining n-r letters. Thus it is clear that the number of the r-permutations of n things is the same as the number of ways in which r numbers can be added to a row originally containing n--r zeros. 2. Hence we can prove the formula Pr = n(n-)(n-2)... (n-r+l). For starting with n-r zeros, we can put the first number at either end of the row, or in any of the n-r-I places between two successive zeros, i.e., we can add the first number to the row in n-r+l different ways. The next number can then be added in n-r+2 ways, giving a total of (n-r+l). (n-r +2) ways of addin...


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Product Details
  • ISBN-13: 9781130446173
  • Publisher: Rarebooksclub.com
  • Publisher Imprint: Rarebooksclub.com
  • Height: 246 mm
  • No of Pages: 32
  • Spine Width: 2 mm
  • Width: 189 mm
  • ISBN-10: 1130446174
  • Publisher Date: 01 Mar 2012
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Weight: 77 gr

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