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**mrpace****Member**- Registered: 2012-08-16
- Posts: 63

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

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That is 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

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**mrpace****Member**- Registered: 2012-08-16
- Posts: 63

Agnishom wrote:

That is sad....

it's not the same question!

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 15,937

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.

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