Recent content by garyljc

Alright thanks a lot =D .

Hey , I was wondering if anyone could help me out with this question regarding calculating the radius of convergence of the infinity series of (1/n!)x^(n!) This is my work First we consider when abs(x) < 1 then we have 0 <= abs(x^n!) <= abs(x^n) so we know that the series converges...

Question : The masses of blocks A and B are given M_a and M_b , respectively, the moment of inertia of the wheel about its axis is I , and the radius of the semicircle in which the string moves is R. Assume that there is no slippage between the wheel and the string. Also M_a > M_b a.) Find...

Just have a question if U,V and W are over the same field K does it mean that dim U = dim V = dim W ?

This is my second attempot oon it im(TS) is a subspace of im(T) and im(T) is a subspace of W therefore rank(TS) =< rank (T) is it correct ? but isn't im(T) = W ?

I came across a question saying Let S: U -> V and T:V -> W be linear maps, where U V and W are vectors spaces over the same field K Show that Rank(TS) =< Rank(T) This is my attempt the im(TS) is a subspace of W and so is the im(T) am I missing out something ?

What does it means by closed under addition For eg : As S is closed under addition S = {gn : n is a member of integers} could anyone elaborate more on this and gimme some example ? Does it mean that when something is closed under addition , we only consider addition and nothing else ?

OK thanks One more question what's the difference between Lim sup a(n) and sup A(n) does the limit tells me something else ?

By definition, a sequence a(n) has the Cauchy sequence if for eery E>0 ,there exist a natural number N such that Abs(a(n) - a(m) ) < E for all n, m > N Could anyone tell me what is a(m) ? is it a subsequence of a(n) , or could it be any other non related sequence ?

but it reads here from my notes that the definition is stated as i said ... could i then have a correct definition of a sequence that tends to infinity ?

what do you mean what's my definition ? tends to = eventually ?

the theorem is as stated that 1. suppose a(n) tends to a and b(n) tends to b , where a and b are constants prove that a(n) + b(n) tends to a+b what approach should i use ? i was thinking about the definition of null sequences

i got question 2 does is this statement true : that for any bounded sequence, it cannot tend to infinity ? for question 1 , a sequence tend to infinity for every C>0 , there exist a nat no. N such that a(n) > C whenever n>N what do you mean i have not said what is C ? isn't c just a number ?

got it ! =)

question 1 : Prove that a sequence which is bounded above cannot tend to infinity What i did was state the definition ... but I'm trying to proof by contradiction. So i first suppose that a(n) tends to infinity , then a(n) > C . But since it is bounded above , C < or = to U , where U is the...