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  1. M

    Given positive interger N, now many non-decreasing sequences of length

    Re: Sequence are the entries positive integers?
  2. M

    I want to understand intuitively why LCM(a,b)=ab/GCF(a,b)

    in your example you have completely ignored prime factorization. suppose we write a number as a list of exponents n=(e1,e2,e3,...) where only finitely many ei's are non-zero, and so that e1 is the exponent of 2, e2 is the exponent of 3, and en is the exponent of the nth prime. in your example...
  3. M

    First step of this simple limit problem

    Re: First step of this simple "limit" problem l'hospital's rule applies nicely. if you haven't learned that, then just factor the numerator and denominator.
  4. M

    Can you beat Roulette using maths?

    say you go to the casino every week with $127 and play a game that pays 1:1. You start by betting a dollar, double your bet with every loss, and start back at a dollar with every win. So, you would need to win 127 times without hitting a streak of seven losses. What would your probability of...
  5. M

    Math paradox?

    The world series would be pretty boring if there was only one team there :) Also, there is a 0% chance there's two teams from LA because the yankees are going.
  6. M

    Group theory problem

    Suppose there is another prime q that divides the order of the group and show there must be an element of order q.
  7. M

    Tidy up with my summary notes

    Re: Group. a number cannot be closed. sets are closed if they contain all their limit points. the set you list is not closed, since 12 is a limit point and 12 is not in the set.
  8. M

    Schools What are my Grad school prospects?

    Re: What are my Grad school prospects?!? That's a great metaphor. Also, Tobias Funke might be the best forum name I've ever seen. "The Man Inside Me" haha.
  9. M

    Schools What are my Grad school prospects?

    Re: What are my Grad school prospects?!? perhaps as important as grammar and spelling is the ability to know your audience. the internet audience is different from a scholastic audience
  10. M

    Schools What are my Grad school prospects?

    Re: What are my Grad school prospects?!? vanadium is right. while there is a vocabulary portion on the GRE test, the admissions board doesn't actually look at it. rather, they go back and check all your old forum posts and make sure you capitalized your 'i's.
  11. M

    Proving a group is abelian

    can you be more clear on how you got this? the inductive step as far as a i can see would be: suppose (xy)^{3k} = x^{3k}y^{3k}. then (xy)^{3(k+1)}= x^{3k}y^{3k}x^{3}y^{3}. but then what... edit: wait i think i got it x^{3k}y^{3k}x^{3}y^{3} =...
  12. M

    Proving a group is abelian

    if G is a group such that (xy)^{3} = x^{3}y^{3} for all x,y in G, and if 3 does not divide the order of G, then G is abelian. I proved an earlier result that said if there exists an n such that (xy)^{n} = x^{n}y^{n} (xy)^{n+1} = x^{n+1}y^{n+1} (xy)^{n+2} = x^{n+2}y^{n+2} for all x,y in G...
  13. M

    How can I explain math to someone who doesn't know math?

    ug...nothing is worse than when i'm reading an algebra book and they say "oh yeah I took algebra in high school." even people that know i've taken a lot of math will say it. do they think i've been studying math at school for years and am still at the same place they were in high school? i...
  14. M

    Show every group of order 77 has elements of order 7 and 11

    I am just looking at this again after a long while, does this work? Let G be a group of order 77. If G is cyclic we're done. If not, then either the hypothesis holds or all elements have order 7 or they all have order 11 (excluding the identity). Supposing all non-identity elements have order...
  15. M

    Brain teaser I can't get out

    lol. suppose no one was at the party. then all of the hypothesis hold vacuously. i don't claim that this is a unique solution, and most likely not the intended one.
  16. M

    Brain teaser I can't get out

    there was no one at the party of course!
  17. M

    Checking commutativity property with addition table

    when they say there is a reflection along the main diagonal they mean that entry i,j = j,i, (i.e. i + j = j + i, the definition of commutivity. it's not just magic!) which you can see is happening here.
  18. M

    Checking commutativity property with addition table

    For one the property a+(b+c) = (a+b)+c is the associative property not the commutative property. The commutative property is ab = ba. I can't see your picture yet, but the table should look like 01234 12340 23401 34012 40123 Where the entry in the position i,j is i + j (mod 5). This table is...
  19. M

    How is (0,1) not compact?

    consider the family of open sets of the form (1,1/n) where n = 1,2,... note the definition of compact is that EVERY open cover contains a finite subcover. edit: oops that should be (1/n,1) of course!
  20. M

    A very basic question: can the null set be the domain of a function?
  21. M

    'Fractional Calculus I' !

    I always wondered what would happen if you substituted values other than integers (and replacing factorials with gamma functions) in cauchy's differentiation formula. Would this give the fractional derivative in the sense you guys are talking about?
  22. M

    Show every group of order 77 has elements of order 7 and 11

    That doesn't complete the proof, for it doesn't handle the case where there is an element of order 7 but not 11 and vice versa.
  23. M

    Show every group of order 77 has elements of order 7 and 11

    Without Sylow's theorems!! This was a problem at the end of a chapter on Lagrange's theorem. I know that every subgroup of order 77 is cyclic. But I don't know how to prove this using only Lagrange. Any suggestions?
  24. M

    Getting phi of a large number

    also since phi is multiplicative phi(a*b) = phi(a)*phi(b) when gcd(a,b)=1
  25. M

    Laplace Transform Problem - Peacewise Functions

    except f(t) isn't 1, read the post again. for piecewise functions use the unit step (heaviside) function.
  26. M

    Wilson's Theorem remainder

    you know that (p-2)! = 1 (mod p). So (p-3)!*(p-2) = 1 (mod p). In this situation, 34!*35 = 1 (mod 37). Call 34! 'x' and then solve 35x = 1 mod 37, which has a unique solution since gcd(35,37) = 1.
  27. M

    General form of prime no.s

    4n+/-1 6n+/-1 is composite iff there are nonzero integers a and b such that n = 6ab + a + b. for instance 6(4) + 1 is composite since 4 = 6(-1)(-1) + (-1) + (- 1)
  28. M

    Help for this infinite integral question ?

    I can't imagine your parentheses are correct...
  29. M

    Morphism which preserves convolution?

    Just looking I would say if you defined G(f) = ln(F(f)), then you would have G(f*g) = ln(F(f)F(g)) = ln(F(f)) + ln(F(g)) = G(f) + G(g). Right?
  30. M

    Laplace transforms of Heavyside functions

    to take the laplace transform of the heaviside function, you want it to be of the form f(t)H(t). Since 2tH(t-1) isn't of this form, the author uses some simple algebra to get something that is.