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

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

**mrpace****Member**- Registered: 2012-08-16
- Posts: 54

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

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'

'You have made another human being happy. There is no greater accomplishment.' -bobbym

Offline

**mrpace****Member**- Registered: 2012-08-16
- Posts: 54

Agnishom wrote:

That is sad....

it's not the same question!

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,544

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

Offline

Pages: **1**