real bitch induction question (1 Viewer)

[blackfriday]

prove n^2-11n+30 >=0 for n>=1

im having a memory blank atm.

thanks

 

[Templar]

Obvious for n=1.

If true for n=k, then for n=k+1

(k+1)^2-11(k+1)+30
=k^2-9k-20
=(k-4)(k-5)
>=0 for all N

 

[Archman]

just one problem mate, thats not induction, u never used the fact that its true for n=k
i mean u may as well just say k^2-11k+30 = (k-5)(k-6) >= 0 for all N

its not really a induction question. But if u really really really really really want to use induction on it,
u can show the cases for n=1,2,3,4,5 (take a while i know)
now assume true for n=k>=5, for n=k+1
(k+1)^2-11(k+1)+30
= (k^2-11k+30)+2k-10
now we know that first bracket is postive by assumption. since k>=5, 2k-10>=0
so the whole thing is positive. (yes its pretty crappy to do a non induction question with induction.)

 

[Trev]

its pretty crappy doin an induction q with induction!

 

[blackfriday]

thats like strong induction isnt it?

 

[Templar]

u may as well just say k^2-11k+30 = (k-5)(k-6) >= 0 for all N

True, wasn't exactly thinking when I wrote the proof.

Anyway, it is a stupid question to do by induction.

 

[Archman]

thats like strong induction isnt it?

nope. thats just induction.

 

[wanton-wonton]

what the fuck is strong induction?

whats the difference between normal induction?

 

[acmilan]

You might have or have not seen or done induction in two ways, whilst browsing through uni notes i saw there are two methods of induction, one which is stronger and one which is weaker

 

[withoutaface]

what the fuck is strong induction?

whats the difference between normal induction?

Weak induction involves assuming the statement is true for n=k
Strong induction involves assuming the statement for all positive integers n=< k

Ivan please correct this if I'm wrong

 

[acmilan]

From what i gathered:

Weak form:
- prove p(1) is true (or whatever the condition is)
- prove p(k+1) is true whenever p(k) is true

Strong form:
- prove p(1) is true (or whatever the condition is)
- prove p(k+1) is true whenever p(m) is true for all m < k

 

[Numero Uno]

?? this makes no sense to me ??

can u elaborate further?

 

[acmilan]

Probably better for someone who has actually done it to explain

 

[wanton-wonton]

strong induction isnt neccessary for HSC right? 'cause i have never heard of it until today....issit uni stuff?

 

[Archman]

strong induction isnt neccessary for HSC right? 'cause i have never heard of it until today....issit uni stuff?

na you dont need it at all.

 

[Archman]

?? this makes no sense to me ??

can u elaborate further?

Ok i'll give a really dumb example to clarify:
given a₁=0 and a_k=a_k-1a₁+a_k-2a₂+a_k-3a₃...+a₁a_k-1 for k>1

prove that all a_n=0 for n>=1

ye, it is not doable with normal induction (despite its dumbness), but can be done with strong induction.

 

[JamiL]

who cares, worry about it if/and when u need 2 in UNI... u could also learn further fuked up calculs that u learn in uni. or further conics or sum other fuked up sit that u would waste ur tym with.

 

[acmilan]

who cares, worry about it if/and when u need 2 in UNI... u could also learn further fuked up calculs that u learn in uni. or further conics or sum other fuked up sit that u would waste ur tym with.

It was only being discussed because someone wanted to know the difference. But yes, dont bother unless you want some extra stuff that you dont need

 

[withoutaface]

Hooray for extra stuff!

 

[a_sea_of_names]

uhh, it's hard ta breathe with Wilsons hand around my throat
uhh, strangled and mangled another SS Curtain call...
when I tried ta cross the white walls

when i tried ta cross the white walls

Walk unseen past tha graves and tha gates
born without a face
One motive no hope, uhh
Born without a face


/i hope thats what your name refers to (directed at without a face...)