Recent content by Norwegian

  1. N

    Identify This Real Number

    And what do you get if you compute e+pi/4 to 22 decimal places?
  2. N

    Novel Multiplication and Division by odd squares

    Yes, removing all unnecessary notation, the result your are looking for is the following: Let k be a real number. For real numbers n and x, define n\circx=nx+k(x-1). Then (n\circx)\circy=n\circ(xy). The proof of this is trivial, and your result is the special case of k=-1/8, and where...
  3. N

    Partitioning of transcendentals

    Hi Robert, Your notion of "width" is of course not well defined. Your idea of distinguishing between numbers with finite and infinite "width" is not a new one. For example, the notion of a definable real number, does perhaps capture your idea, and more. It is an elementary fact that...
  4. N

    A representation using reciprocal primes

    Hi Robert, My first question about this is: What is the significance of prime numbers here? Could you just as well use any increasing sequence of natural numbers for which the sum of the reciprocals diverges?
  5. N

    Are the following 3 statements true and does the cantor-bernstein theorem follow

    No. 1) and 2) are definitions of ≤ and ≥ for cardinalities of sets. 3) is a nontrivial consequence for which you have provided no argument at all.
  6. N

    Equivalence between a set and the subset of its subset

    You should consider also informing us about the relevant equivalence relation, as the truth or falsity of your statement heavily depends on that information. For example, if you for your eq.rel. use existence of a bijection, the statement is true, but other relations, like having same parity...
  7. N

    Matrices satisfying certain relations

    Hi Aija, your statement above is just wrong. From those 3 equations, you should immeditately observe the solution a=b=c=M, where M is any invertible matrix, and the "problem" is to determine the remaining solutions, if any.
  8. N

    Stuck on simple algebra problem

    This becomes correct if you replace the last w with w'
  9. N

    Having some trouble with this combinatorics problem

    You are asking about the number of derangments Sn of a set with n elements. If you are looking for an exact answer, you can either use the recurrence relation Sn+1=n(Sn+Sn-1), or compute the alternating sum Ʃ(-1)in!/i! where i goes from 0 to n.
  10. N

    Powers of matrices equal to the identity matrix

    A solution to An=I is obviously attained if A is a suitable diagonal or rotation matrix, and also for all similar matrices PAP-1, where P is invertible.
  11. N

    Combinatorics Problem: Solving Geometric Angle Challenges with Addition

    Hi, msmath, are you serious about any of the above? I find it all completely incoherent. Would you mind explaining in complete sentences what is going on, and what your motivation for this is?
  12. N

    Constructing an Edge in Progressive Betting Systems for Coin Toss Events

    Hi there, would you mind informing us of your proposed betting procedure, an in particular how you arrive at your numbers? And again, since your coin is fair, and I suppose you are given fair odds on each bet, all bets, both individually and collectively, will have zero EV. That is a fact...
  13. N

    Interesting thing I've noted

    Hi there, you have observed some cases of powers of 2 being almost in the middle of consecutive squares, and you ask about the next occurence. A quick computer search reveals no such cases with exponent less than 1000. So unless either I or my computer made a mistake, which may very well happen...
  14. N

    Constructing an Edge in Progressive Betting Systems for Coin Toss Events

    Sure, but then the probability of getting H or T in (1) must be 100%.
  15. N

    Showing that a limit does not equal some value

    The answer is no. The only value for x satisfying the above requirement is x=c, and whether or not f(c) is defined is irrelevant for the existence of the limit.
Back
Top