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

Anthony.R.Brown wrote:

Any so called Proof by induction! is still only Guess work! whether it is 150 pages or 150 million pages! size don't matter if you can't see the actual end of something 100%.....

a good example is " I state that in the sequence 1,2,3,4,5,6,7,8,9...for as far as we can see the numbers will always end in an Odd Number!

but if I could see a bit further! " I state that in the sequence 1,2,3,4,5,6,7,8,9,10...for as far as we can see the numbers will always end in an even Number!

Both examples above are by induction!........but neither is 100% correct or a Proof!.............

I'm not an expert at the definitions of proof by induction, but I'm pretty sure that a single example is not a proof. Otherwise I could come up with all sorts of "proofs"

5 is a number. 5 is odd. Therefor all numbers are odd.

-4 is a number. -4 is less than 0. Therefor all numbers are less than 0.

So saying that a single sequence of numbers ends with an odd number, means that all sequences of numbers end with an odd number isn't proof of anything.

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

To Maelwys..etc...

Deductive reasoning is the kind of reasoning in which the conclusion is necessitated by, or reached from, previously known facts (the premises). If the premises are true, the conclusion must be true. This is distinguished from abductive and inductive reasoning, where the premises may predict a high probability of the conclusion, but do not ensure that the conclusion is true. For instance, beginning with the premises "All ice is cold" and "This is ice", you may conclude that "This is cold".

Deductive reasoning is dependent on its premises. That is, a false premise can possibly lead to a false result, and inconclusive premises will also yield an inconclusive conclusion.

A.R.B

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

Anthony.R.Brown wrote:

Any so called Proof by induction! is still only Guess work

No it isn't, it's an induced proof, HENCE proof by induction.

Anthony.R.Brown wrote:

a good example is " I state that in the sequence 1,2,3,4,5,6,7,8,9...for as far as we can see the numbers will always end in an Odd Number!

That's not an example of induction, you don't understand what you're talking about.

Anthony.R.Brown wrote:

Both examples above are by induction!

No they aren't

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

Quote:" No they aren't "

A.R.B

Yes they are!!

Both are examples to show depending on how far it is possible to look at a Sequence of Numbers! the Result can be Different!

For my examples! generalization, judgment, logical reasoning has been used by showing the sequence from the Start onwards!

Main Entry: induction

Part of Speech: noun 2

Definition: inference

Synonyms: conclusion, conjecture, generalization, judgment, logical reasoning, ratiocination, rationalization, reason

Source: Roget's New Millennium Thesaurus, First Edition (v 1.3.1)

Copyright © 2007 by Lexico Publishing Group, LLC. All rights reserved.

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

Anthony.R.Brown wrote:

Quote:" No they aren't "

A.R.B

Yes they are!!

Both are examples to show depending on how far it is possible to look at a Sequence of Numbers! the Result can be Different!

For my examples! generalization, judgment, logical reasoning has been used by showing the sequence from the Start onwards!Main Entry: induction

Part of Speech: noun 2

Definition: inference

Synonyms: conclusion, conjecture, generalization, judgment, logical reasoning, ratiocination, rationalization, reason

Source: Roget's New Millennium Thesaurus, First Edition (v 1.3.1)

Copyright © 2007 by Lexico Publishing Group, LLC. All rights reserved.

In english, you are correct. However, we're speaking about Math here, which has it's vocabulary that is much more specific about the meanings of terms.

From Wikipedia - Mathmatical Induction:

"Mathematical induction is used to prove that every statement in an infinite sequence of statements is true. It is done by

* proving that the first statement in the infinite sequence of statements is true, and then

* proving that if any one statement in the infinite sequence of statements is true, then so is the next one"

Your "proof" doesn't fit this definition, because you're only proving that the first statement is true, but not that the next statement is also true.

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**Devantè****Real Member**- Registered: 2006-07-14
- Posts: 6,400

Anthony.R.Brown wrote:

To Maelwys..etc...

Deductive reasoning is the kind of reasoning in which the conclusion is necessitated by, or reached from, previously known facts (the premises). If the premises are true, the conclusion must be true. This is distinguished from abductive and inductive reasoning, where the premises may predict a high probability of the conclusion, but do not ensure that the conclusion is true. For instance, beginning with the premises "All ice is cold" and "This is ice", you may conclude that "This is cold".

Deductive reasoning is dependent on its premises. That is, a false premise can possibly lead to a false result, and inconclusive premises will also yield an inconclusive conclusion.

A.R.B

You just copied that from here.

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

Quote:" You just copied that from here. "

A.R.B

Wrong!! from here http://thesaurus.reference.com/

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

Quot:"Your "proof" doesn't fit this definition, because you're only proving that the first statement is true, but not that the next statement is also true. "

A.R.B

Every Number in the Sequence is true from 1,2,3,4,5,6,7,8,9 ....

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**Devantè****Real Member**- Registered: 2006-07-14
- Posts: 6,400

So, these kinds of things make a difference to you? In reality, a lot of resources are taken or 'broken from' other informative sources.

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

Anthony.R.Brown wrote:

Every Number in the Sequence is true from 1,2,3,4,5,6,7,8,9 ....

Nobody even knows what to make of that sentence.

"Every number in this sequence is true"?

You have no idea how to apply induction, stop making things up.

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

a good example is " I state that in the sequence 1,2,3,4,5,6,7,8,9...for as far as we can see the numbers will always end in an Odd Number!

but if I could see a bit further! " I state that in the sequence 1,2,3,4,5,6,7,8,9,10...for as far as we can see the numbers will always end in an even Number!

The point is!!

Based on the two Sequences above the results are Different! because of how far we can Calculate! the same applies to any Infinite Sequence or Calculations, the end result whether using a large sample induction or a small sample as I have done,can never show a 100% Proof because there will always be some Information missing!

INDUCTION CAN ONLY EVER BE A DEMONSTRATION!

A.R.B

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

Anthony.R.Brown wrote:

a good example is " I state that in the sequence 1,2,3,4,5,6,7,8,9...for as far as we can see the numbers will always end in an Odd Number!

but if I could see a bit further! " I state that in the sequence 1,2,3,4,5,6,7,8,9,10...for as far as we can see the numbers will always end in an even Number!The point is!!

Based on the two Sequences above the results are Different! because of how far we can Calculate! the same applies to any Infinite Sequence or Calculations, the end result whether using a large sample induction or a small sample as I have done,can never show a 100% Proof because there will always be some Information missing!

INDUCTION CAN ONLY EVER BE A DEMONSTRATION!

A.R.B

The point is, neither of those is an inductive proof. To make an inductive proof you need to prove that something is true for both n and n+1. Those are both just single statements (basically saying that if n=9 it's true, but not proving that it's true for n+1), that don't carry any proof at all.

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

To Maelwys

Quote:"The point is, neither of those is an inductive proof. To make an inductive proof you need to prove that something is true for both n and n+1. Those are both just single statements (basically saying that if n=9 it's true, but not proving that it's true for n+1), that don't carry any proof at all."

A.R.B

n = 1 n+1 = 1,2 n+1+1 = 1,2,3 and so on! so the same as you are saying!.

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

Anthony.R.Brown wrote:

To Maelwys

Quote:"The point is, neither of those is an inductive proof. To make an inductive proof you need to prove that something is true for both n and n+1. Those are both just single statements (basically saying that if n=9 it's true, but not proving that it's true for n+1), that don't carry any proof at all."

A.R.B

n = 1 n+1 = 1,2 n+1+1 = 1,2,3 and so on! so the same as you are saying!.

Now you're no longer proving that number is odd though. For n, the number is odd. For n+1 the number is even. So it's no longer a proof of anything.

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

To Maelwys

Quote:" Now you're no longer proving that number is odd though. For n, the number is odd. For n+1 the number is even. So it's no longer a proof of anything. "

A.R.B

you must now be agreeing with what i'm saying! the Number Sequence is either Odd or Even depending on how far we Calculate!..............the problem cant be Reduced by Induction!

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

Anthony.R.Brown wrote:

To Maelwys

Quote:" Now you're no longer proving that number is odd though. For n, the number is odd. For n+1 the number is even. So it's no longer a proof of anything. "

A.R.B

you must now be agreeing with what i'm saying! the Number Sequence is either Odd or Even depending on how far we Calculate!..............the problem cant be Reduced by Induction!

ummm... okay.

I agree that what you're trying to do doesn't prove anything by induction. But I don't agree that this means that nothing can be proved by induction.

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

Anthony.R.Brown wrote:

you must now be agreeing with what i'm saying! the Number Sequence is either Odd or Even depending on how far we Calculate!..............the problem cant be Reduced by Induction!

You never attempted to induce it, furthermore, it's non-sensical.

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

Anthony.R.Brown wrote:

To Maelwys

Quote:" Now you're no longer proving that number is odd though. For n, the number is odd. For n+1 the number is even. So it's no longer a proof of anything. "

A.R.B

Very good Anthony, induction can't be applied to everything. If I want to find out what color my math book is, I can try as hard as I want, but induction will (hopefully) never give me the answer. Similarly, if I wish to find out if 4827473 is prime, I probably can't use induction.

Now, can you try to use an example in which *induction can actually be applied*?

"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

To Ricky

Quote:" Now, can you try to use an example in which induction can actually be applied? "

A.R.B

Induction can be applied to many things! my Argument originally is that Induction can't give a 100% Proof to anything if there is any Information missing! ie. if we can't see the end of a Calculation then we can only Guess the result!!...........................................................

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

you really *aern't* getting this anthony.

are you saying that with induction you cannot prove that sum of the first 'n' numbers starting with 1 is 0.5n(n+1) because you can't test it with everysingle possible value of 'n'? That is what induction is for, induction allows you to do so, because you dont need to prove it for every value, because you can prove that if one value is true, then the next will be true, and then from one single result, you can induce all other results

*Last edited by luca-deltodesco (2007-05-29 01:29:20)*

The Beginning Of All Things To End.

The End Of All Things To Come.

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

To Luca-deltodesco

Quote" you really aern't getting this anthony.

are you saying that with induction you cannot prove that sum of the first 'n' numbers starting with 1 is 0.5n(n+1) because you can't test it with everysingle possible value of 'n'? That is what induction is for, induction allows you to do so, because you dont need to prove it for every value, because you can prove that if one value is true, then the next will be true, and then from one single result, you can induce all other results "

A.R.B

You really aern't getting! IT!!

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

which as I have said many times is only a DEMONSTRATION!

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

Anthony, why can't you just admit that you don't understand concepts that are above your mathemtical capability? You're just trolling, stop it.

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**George,Y****Member**- Registered: 2006-03-12
- Posts: 1,315

Anthony.R.Brown wrote:

To Maelwys..etc...

Deductive reasoning is the kind of reasoning in which the conclusion is necessitated by, or reached from, previously known facts (the premises). If the premises are true, the conclusion must be true. This is distinguished from abductive and inductive reasoning, where the premises may predict a high probability of the conclusion, but do not ensure that the conclusion is true. For instance, beginning with the premises "All ice is cold" and "This is ice", you may conclude that "This is cold".

Deductive reasoning is dependent on its premises. That is, a false premise can possibly lead to a false result, and inconclusive premises will also yield an inconclusive conclusion.

A.R.B

Very clear logic, and I don't get why so many people are objecting him.

**X'(y-Xβ)=0**

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

Anthony.R.Brown wrote:

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

which as I have said many times is only a DEMONSTRATION!

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

Call if what you will, but the rest of the math world accepts mathematical induction as a method of proof. I don't believe it's been wrong yet, as long as it's being properly applied. And the above example is a valid one.

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

George,Y wrote:

Very clear logic, and I don't get why so many people are objecting him.

because that's copied and pasted, but more importantly it's arguing against him.

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