1. ISP

    Enumerating An Uncountable Ordinal

    Disclaimer: I have a sense of humor and a purpose, so I’m going to try and enumerate $\omega_1$ itself. Clearly that is a crankish proposition, so this disclaimer is meant to clarify what I mean to accomplish and acknowledge that there should obviously be an error if I conclude that I have...
  2. idontknow

    Comparing large numbers without calculus

    A curious logical consequence of the principle of non-contradiction is that a contradiction implies any statement; if a contradiction is accepted as true, any proposition (or its negation) can be proved from it. Let's try (*)66^{77} > 77^{66} . I will prove (*) using sgn function(analytic...
  3. K

    Linear combination of random variables, convergence for a large number of variables

    Hi, I have positive random variables X1, X2, X3, ..., Xn such that their sum=1 (so they are random, subject to constraints that each Xi is positive their sum has to be 1.. so all are fractions). Now, I have a function f=C1.X1+C2.X2+C3.X3.....+Cn.Xn where C1, C2, ....Cn are known...
  4. K

    Law of large numbers

    I have a question in statistics. I am a Chemical Engineer (reaction chemistry research). In an example reaction experiment, the feed to a reactor consists of n compounds with mass fractions X1, X2, ... Xn so that: X1+X2+X3+...+Xn=1 This feed goes into the reactor with constant temperature...
  5. F

    Large number divisible

    Find the largest integer k such that k divides n^55-n for all integer n?
  6. L

    Prime Factorization of very large integer with quadratic residue and its square roots

    We have a very large modulus integer n also we have very large number y we know that y is a quadratic residue modulus n.Also we know all 4 square roots of y. What is the best way of prime factorization of n ?
  7. M

    Factoring large odd/uneven numbers?

    I fell into this problem when trying to figure out a way to subtract fractions with big uneven denominators, and am stuck. How do we use prime factorization for numbers like this? 2/57 - 9/67 Is it okay if you get fractions in prime factorization? What should I do? Thank you!
  8. T

    Prove a large number of samplings converge to a set of small number of samples

    In a $k$-dimensional space, given a set of $n$ points: $X=\{x_1, x_2,..., x_n\}$ which is sampled from an known distribution $P$. Given a set of $m$ points ($m << n$): $Y=\{y_1,y_2,...,y_m\}$ which is also drawn from $P$. Suppose $\{z_1, z_2,...,z_m\} \subset X$ are the closest points (in term...
  9. M

    ratios with large numbers

    i would like to know the ratio between these two GDPs 21582 and 21003 and then 18874 and 20261. thanks ma
  10. J

    large numbers?

    So I heard that graham's number for example was considered the largest named number in 1975, but I also read that there were other larger numbers then (like graham's number with 4's instead of 3's) as well as functions like the ackermann function. My question is, did mathematicians use large...
  11. N

    easy way to subtract large numbers

    Hi, I am looking for an easy way to subtract large numbers without the use of a calculator. Numbers such as: 717299874, 238303931, 279890276, 215879628, 359239774, 825753868, 928942504 Any tips? Thanks, Neta.
  12. G

    finding the cube of large numbers?

    Is there a way to figure out these larger numbers I get how to do the variables though so far. Thanks.
  13. M

    Large deviation function for a Gamma distribution

    I have a problem with the final part of this exercise. I have computed the large deviation function of that distribution correctly, I've also found the form of the Y function but I'm not able to justify that relation. Could anyone explain it to me please? Compute the large deviation function...
  14. F

    Dimensions of small boxes in the large box

    Hi, Dimensions of large box: 38x27x37 Quantity of small boxes in large box: 100 Packed tight, no free space. How to calculate the size of a small box? Thanks
  15. G

    The smallest angle in a triangle is 1 5 15 as large as the largest angle. The third

    Ouch! this hurts! The smallest angle in a triangle is 1/5 as large as the largest angle. The third angle is twice the smallest angle. Find the three angles. trying to get rid of fraction before solving if possible. As fractions really hurt me. so i am guessing I first need to go 5/5...
  16. I

    Number of factors of a large number

    Find the number of factors of 10004000600040001
  17. J

    Are large numbers definable?

    So I've been looking up large numbers lately and my question is, can we even define some of those? A lot of the information I read looking them up seems pretty inconsistent. For example, I remember seeing a page that prints out a googolplex on the screen, while there are supposedly more digits...
  18. A

    approximate a large network with a smaller network derived from it

    Do any of you happen to know of a good method to approximate a large network with many edges and nodes with a much smaller network derived from it? I have found the following list of papers related to this topic: -Metropolis Algorithms for Representative Subgraph Sampling -A new algorithm...
  19. K

    How do I find the smallest proper divisor of large numbers?

    For example, ( 22! + 1). I can't find examples in books or on the internet. Any help very much appreciated.
  20. K

    iterative solution of large matrix inequality least square

    Hi, I am working on a linear equation (y=a*X). To get the solution, I need to add some inequality constraint like, b1<=AX<=b2. The dimension of X is very high, let's say 10^5 * 10^5. I think I have to use some iterative method. Anybody can provide a solution for me? Many thanks!