Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

#1 2013-04-15 04:38:38

mrpace
Member
Registered: 2012-08-16
Posts: 61

Prove by induction.......

Let f be some given function for which we wish to find a such that
f(alpha)= 0. Suppose that the equation f(x)= 0 may be arranged into
the form x=g(x), such that for some interval (a,b) alpha is in (a,b)  and
g(x) belongs to (a,b) . Further, suppose that g is differentiable with |g'(x)|</= C
for x belonging to (a,b), where C is some positive number. (Note that x=g(x)
implies that alpha=g(alpha)

please note that when i say "belonging to" i mean that symbol that looks a bit like an 'E'

Prove by induction that
|alpha-Xn| </= C^n|alpha-Xo|

thanks

Offline

#2 2013-04-15 04:40:33

Agnishom
Real Member
From: Riemann Sphere
Registered: 2011-01-29
Posts: 21,578
Website

Re: Prove by induction.......

That is sad.... sad


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'But our love is like the wind. I can't see it but I can feel it.' -A Walk to remember

Offline

#3 2013-04-15 04:45:49

mrpace
Member
Registered: 2012-08-16
Posts: 61

Re: Prove by induction.......

Agnishom wrote:

That is sad.... sad

it's not the same question!

Offline

#4 2013-04-15 05:50:43

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,922

Re: Prove by induction.......

What are Xn and X0?


“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

Offline

Board footer

Powered by FluxBB