Question

Verify the triangle inequality

Answer 1

whoops give me time to attache the file

Answer 2

did you try using wolframalpha?

Answer 3

||u +v || is less than or equal to ||u|| +||v||

Answer 4

I have no clue... I'm in A2/Trig not college :P I need a life

Answer 5

|<f,g>| <= |<f,f>|+|<g,g>|

Answer 6

sqrt(<f,g>) <= sqrt(<f,f>) + sqrt(<g,g>)

Answer 7

<f,g> = Integral (x*e^(-x),x,0,1)

Answer 8

noooo u dont sqrt the left hand side

Answer 9

we didnt do that last time

Answer 10

but last time we didn't have |<f,g>|

Answer 11

wait let me think

Answer 12

that is true but remeber what i sent u

Answer 13

sqrt((e-2)/e) <= sqrt(Integral(x^2,0,1)) + sqrt(Integral(e^(-2x),0,1))

Answer 14

Yes i did pippa, be patient and trust me on this one, please? I suck at linear algebra, but I know my topology....

Answer 15

By the way, that was a risky statement, im just gonna disappear, if i get this wrong now.

Answer 16

lol what was a risky statement? lol

Answer 17

i didnt follow what u did. i am soooo slow today

Answer 18

sqrt((e-2)/e) <= sqrt(1/3) + sqrt( (1/2)-( 1/(2e^2) ) )

Answer 19

want me to write that out? The rsiky statement was. I said I knew my topology, if I get this wrong, that means I don't even know topology and I have no right to speak whatsoever.

Answer 20

who cares i will correct u if i feel so lol

Answer 21

haha u dont have to feel responsible

Answer 22

Anyway the right gives u: 1.23487
the left side gives u: 0.51..
0.51 <= 1.23, so the inequality holds

Answer 23

as was to be proven. Where did u get lost?

Answer 24

idk i was doing smth diff arrrgghhhhhh i am f* stupid

Answer 25

Do my eyes deceive me? Pippa, who doesn't like my language on skype?

Answer 26

ya sorry

Answer 27

btw u're not stupid.
||u|| = ||<u,u>|| = sqrt(<u,u>)

Answer 28

So:
||<u,u>|| = sqrt(<u,u>)
||<f,g>|| = sqrt(<f,g>)

Answer 29

ya ur right now i see it :D

Answer 30

<f,g> = Int (f*g) from 0 to 1, so
||<f,g>|| = sqrt(<f,g>) = sqrt(Int(f*g))

Answer 31

ok good

Answer 32

hey thanks