To Sekky "ITS ABOUT TIME YOU SHOWED SOMETHING!"

A.R.B

This is my old trick, but still informative.

Anthony.R.Brown wrote:

To Maelwys

Quote:" Okay, what's the 1 case in 1000 that you can't prove with this? "

A.R.B

you have a shorty memory! 1,2,3,4,5,6,7,8,9..Odd or Even?

is WHAT odd or even?

Anthony.R.Brown wrote:

To Maelwys

Quote:" Okay, what's the 1 case in 1000 that you can't prove with this? "

A.R.B

you have a shorty memory! 1,2,3,4,5,6,7,8,9..Odd or Even?

You left off part of my quote. "I don't believe it's been wrong yet, as long as it's being properly applied."
Whatever your 1,2,3... example is, it's not a proper application of mathematical induction.

I think it's time for a word from one of my old lecturers.

Induction is an axiom: in other words, if you don't believe it, there is not much I can do except advise you to study astrology instead.

He later went on to talk about goldfish that needed the whole of history recited to them every morning at breakfast, and how elephants were more useful. He was so great.

Anyway, I'm interrupting your debate. Just ignore me.

Anthony, define your proposition, P(n), of the example you seem to be using.

Oh, by the way, failure to do so will just invalidate your claim, so drop the ad-hominem and just do it.

Oh boy. Anthony is now refuting π as a number.
You're right in that you can't give the full decimal answer of any problem whose solution involves π, because you'd have to make an approximation, but it's perfectly allowed to work out answers by just leaving π as a symbol.

Ricky, I'm not sure what you mean. It seems like you're saying that induction works because it is defined that way, which doesn't make any sense. Also, didn't someone say earlier that it was a Peano axiom?

Anthony.R.Brown wrote:

For the Sequence 1,2,3,4,5,6,7,8,9.......etc. It's Impossible for Induction to Prove if the Number Sequence will End as an Odd Number or an Even Number!.....................................................

There's two reasons for that:
1/ There is no end to an infinite sequence
2/ Inductive proof fails (n=odd, n+1=even). Induction can't prove everything, and nobody is claiming that it can. All we're saying is that in cases that you CAN use mathematical induction, it IS a valid proof that is 100% correct.

Anthony.R.Brown wrote:

To Maelwys!

A.R.B

Dont tell me! tell Sekky! ( The Mirror Man/Person? )

Tell him what? I'm pretty sure he agrees with me. That's why he was asking you to show him a formula for a valid proof by induction [the P(n) he was asking about] that wasn't 100% proof. You were the one saying

Anthony.R.Brown wrote:

for 1 is 0.5n(n+1) you can only prove it 99.9% of the time!

Which is why we were asking what 1/1000 cases of THAT induction are not provable.

Anthony.R.Brown wrote:

To Maelwys

Quote:" Which is why we were asking what 1/1000 cases of THAT induction are not provable. "

A.R.B

The 1/1000 + 1 + 1 etc.......................................................................................................

Huh?

I'm not even sure what that's supposed to represent...

Oh, and by the way. An ellipsis generally only requires 3 dots, not 33. The extra copies don't make it any more or less significant.

oh you!

The Induction Challenge!
------------------------------------------------------------------------------------------------

Anyone like to try and put forward a 100% Proof for any Math Problem/Calculation

Where the Problem/Calculation contains ( Pi ) within it!

A.R.B

To ephemere

Quote:" I just happened upon this ridiculous thread while googling something.

Claim: n > π for all integers n >= 4.

Proof:
n = 4: 4 > π.
n > 4: Assume n-1 > π.  Then n > n-1 > π. "

A.R.B

Can you prove the Value of Pi