Hai,

I need help with his one, it's pretty simple and im pretty darn lousy at math :)

Show that for all positive integers n, and

all real numbers x

It's true for

But im stuck at the inductive step:

Please help?

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- October 6th 2009, 09:43 AMJonesInductive proof
Hai,

I need help with his one, it's pretty simple and im pretty darn lousy at math :)

Show that for all positive integers n, and

all real numbers x

It's true for

But im stuck at the inductive step:

Please help? - October 6th 2009, 10:18 AMPlato
- October 6th 2009, 10:20 AMJones
- October 6th 2009, 10:25 AMPlato
- October 6th 2009, 10:27 AMJones
- October 6th 2009, 10:35 AMPlato
We prove that induction "works" by the use of the fact the positive integers are

*well ordered*with respect .

That is, ‘every non-empty subset of positive integers contains a least element’.

But the real numbers are well ordered with respect .

The real number set contains no least element. - October 6th 2009, 11:24 AMJones
- October 6th 2009, 11:25 AMaman_cc
What Plato said - is little more in a formal language with deeper concepts. If you are new to this maybe thinking like this will help

Why does induction work -

a. You prove it for 1.

b. You assume it for some 'n' and based on this assumption prove it will be true for 'n+1'

Now let's combine a and b above. Put n=1, by 'a' this is true for 1. Then by 'b' it is true for n+1(=2). Apply 'b' again and again. You see it is true for 1,2,3,4,5,......**You will 'generate' all the natural numbers**by this procedure. Thus statement is true for all natural number.

Now think, will this work for real numbers? or even rationals? Can by repeatedly adding 1 (or any number) will you be able to list all the real numbers?

Hope it helps - October 7th 2009, 01:36 PMJones
- October 7th 2009, 02:05 PMHallsofIvy
Because

**means**! - October 7th 2009, 02:09 PMPlato