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**Anthony.R.Brown****Banned**- Registered: 2006-11-16
- Posts: 516

To Sekky "ITS ABOUT TIME YOU SHOWED SOMETHING!"

A.R.B

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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,316

tell me

Haha!!!

By induction!!!

**X'(y-Xβ)=0**

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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,316

This is my old trick, but still informative.

**X'(y-Xβ)=0**

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**Anthony.R.Brown****Banned**- Registered: 2006-11-16
- Posts: 516

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?

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**Sekky****Member**- Registered: 2007-01-12
- Posts: 181

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?

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**Anthony.R.Brown****Banned**- Registered: 2006-11-16
- Posts: 516

To Sekky!

A.R.B

You are just too.. for words!......have a look at the Posts and you may also Remember??

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**Maelwys****Member**- Registered: 2007-02-02
- Posts: 161

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.

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**Sekky****Member**- Registered: 2007-01-12
- Posts: 181

Ok, Anthony, let's do it your way, by formal mathematical induction.

Define your proposition P(n), for your case.

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

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.

Why did the vector cross the road?

It wanted to be normal.

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**Anthony.R.Brown****Banned**- Registered: 2006-11-16
- Posts: 516

MATH PROBLEMS INDUCTION CAN'T PROVE 100%

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(1) Math Problems that use ( Pi ) Calculations any where within the Problem.

(2) Any other Infinite Math Problems

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**Sekky****Member**- Registered: 2007-01-12
- Posts: 181

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.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

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.

That's not exactly true. We define the natural numbers with a 5th property, that of induction. We can prove that such a set, in which induction applies, exists. So it isn't an axiom, just a property.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

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?

Why did the vector cross the road?

It wanted to be normal.

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**Anthony.R.Brown****Banned**- Registered: 2006-11-16
- Posts: 516

Quote:" 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. "

A.R.B

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!.....................................................

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**Maelwys****Member**- Registered: 2007-02-02
- Posts: 161

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.

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**Anthony.R.Brown****Banned**- Registered: 2006-11-16
- Posts: 516

To Maelwys!

A.R.B

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

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**Maelwys****Member**- Registered: 2007-02-02
- Posts: 161

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.

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**Anthony.R.Brown****Banned**- Registered: 2006-11-16
- Posts: 516

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.......................................................................................................

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**Maelwys****Member**- Registered: 2007-02-02
- Posts: 161

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.

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**Sekky****Member**- Registered: 2007-01-12
- Posts: 181

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!.....................................................

because it's not induced

And yes, I agree with Maelwys, and I can prove it by induction.

Let M(Maelwys) |-> True

P(n) : (M(Maelwys) = True) implies (Anthony gets argumentative and hormonal)

P(1) is the current thread, hence P(1) is true.

Anthony gets argumentative and hormonal is a universal constant, hence P(n) is invariant under n.

Therefore P(n) implies P(n+1).

Q.E.D

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**luca-deltodesco****Member**- Registered: 2006-05-05
- Posts: 1,470

oh you!

The Beginning Of All Things To End.

The End Of All Things To Come.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

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?

Not quite. We define induction to be the property:

Let N be a set. Let A be a set with the following property: if n is in A, then *S(n) is in A. Induction is the property that if 1 is in A, then A = N.

And we can prove there exists a set which such a property. It's because we are proving the existence of a set with this property which makes it not an axiom.

*S(n) is known as the successor function, simply put, 2 = S(1), 3 = S(2), and so on.

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**Anthony.R.Brown****Banned**- Registered: 2006-11-16
- Posts: 516

The Induction Challenge!

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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

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**ephemere****Member**- Registered: 2007-06-02
- Posts: 2

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.

Or perhaps Anthony thinks there may be some mysterious value of *n* out there for which this proof fails?

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**Anthony.R.Brown****Banned**- Registered: 2006-11-16
- Posts: 516

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

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