greg

I want a good IDE for developing python when i'm out of the office. We use proprietary software there and i'm not interested in buying a program if i don't have to. A good eclipse plugin would be nice, but I have a net-book who is not a big fan on the super bulky eclipse program, so something more lightweight would be better. I work with a bunch of java developers so none of us know a ton about python/jython....

a is an arbitrary constant.

This is from the Taylor polynomial,

it would be, f^n+1(c) * |x - a|^(n+1)/(n+1)!

but i can show the the f^(n+1)(c) is bdd, so now I just need to show convergence to prove the approximation. Instinctively i can tell that this is true.

(I know the o(n^n) contains o(n!) but not vice versa so this must be true, but i'm quite sure asymptotic notation is a terrible way to structure this argument haha.)

I just need help structuring this argument i suppose. my background is computer science not math, so i have trouble with the proofs.

Saw a video online that said that rational numbers were isomorphic to the natural numbers, but i also know that rational numbers are dense, where natural numbers are not. I understand that this should work since we cant use the diagonalization argument to disprove this like on would with the irrationals. I'm just wondering what the argument for the bijection / isomorphism would look like? Is it far to simply map

1 -> 1/1

2 -> 1/2

3 -> 1/3

4 -> 2/3

5 -> 1/4

6 -> 2/4

etc... ?

** I kinda think I answered my own question in the process of asking it, but gonna post it anyway to see what people think.

Let: T = 1 + 2 + 4 + 8 + 16 + 32 + . . .

Thus: 2T = 2 + 4 + 16 + 32 . . .

Thus: 2T - T = -1 + 0 + 0 + 0 + 0 . . .

Thus: T = -1

Therfore : -1 = 1 + 2 + 4 + 8 + 16 + 32 + . . .

This is clearly impossible yet, i see no contradictions in the proof?

does anyone understand this?

been doing java for about three years now, time to move on. What do you recommend?

I have dreams about solving equations in my dreams, And when I'm stressed I usually wake up thinking about some equation that just doesn't work/ is unsolvable and I can't fall back asleep until i get myself to forget about it. The funny things is how bad my unconscious mind is at math, because when i do remember whatever it was i was thinking about, I always do retarded things that don't make any sense.

Any analysis / useful insight

Okay so this is a problem i think i have an answer to but I cant tell... can anyone confirm or refute this?

A weight (17.0kg) hangs from a wire (4m) with negligible mass. The wire is free to rotate 360 degrees. A dart (5.5kg) is shot horizontally at the weight and embeds itself into the mass. What is the minimum speed of the dart required to propel the weight in a full loop.

a.)

Assumptions:

--The initial energy = Ki = (1/2)M*Vi^2

--If the weight make it so the top of the circle it finishes the loop.

--As the velocity approaches the minimum the energy at the top of the loop Kf approaches 0.

--The work done is equal to work of lifting a weight twice the radius of the circle --> W = M*g*10

--Final energy equals initial energy plus work Kf = Ki + W

Thus 0 = (1/2)M*Vi^2 + M*g*10

M = 17+5.5 = 22.5; g = -9.8.

Vi = SQRT((2)(9.8)(8))

b.)

|Vi| is the speed of the weight.

momentum of the weight = mass of the weight * velocity of the weight

momentum of the dart = mass of the dart * velocity of the dart

--> Mw*Vi=Md*Vd so

--> Vd = Md*Vi/Mw

--> Vd = Md*(SQRT(2*g*2R))/Mw

--> Vd = 5.5*(SQRT(2*9.8*8))/22.5

-->3.2 M/s

This seems too low, but i cant see what would be wrong...