Math Is Fun Forum

mrpace

Member

Registered: 2012-08-16

Posts: 88

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

Agnishom

Real Member

From: Riemann Sphere

Registered: 2011-01-29

Posts: 25,002

Website

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

That is sad....

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'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'
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mrpace

Member

Registered: 2012-08-16

Posts: 88

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

That is sad....

it's not the same question!

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

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

What are Xn and X0?

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