Math "Disproofs"
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10-09-2012, 07:18 PM
Math "Disproofs"
If anyone has wondered where I've been for the past week...









Apparently mathematicians didn't stumble across this because they didn't realize that math with infinities was so simple.

Feel free to criticize.

My girlfriend is mad at me. Perhaps I shouldn't have tried cooking a stick in her non-stick pan.
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10-09-2012, 09:05 PM
RE: Math "Disproofs"
(10-09-2012 07:18 PM)Starcrash Wrote:  If anyone has wondered where I've been for the past week...









Apparently mathematicians didn't stumble across this because they didn't realize that math with infinities was so simple.

Feel free to criticize.

1/9 = 0.1111...
2/9 = 0.2222...
3/9 = 0.3333...
4/9 = 0.4444...
5/9 = 0.5555...
6/9 = 0.6666...
7/9 = 0.7777...
8/9 = 0.8888...
9/9 = 0.9999...

Skepticism is not a position; it is an approach to claims.
Science is not a subject, but a method.
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10-09-2012, 09:41 PM
RE: Math "Disproofs"
(10-09-2012 07:18 PM)Starcrash Wrote:  If anyone has wondered where I've been for the past week...









Apparently mathematicians didn't stumble across this because they didn't realize that math with infinities was so simple.

Feel free to criticize.

I think your reflexive list is brilliant. However, it has nothing much to do with the proof.

The heart of a RAA proof is that something is assumed to be true and from this we derive a contradiction.

We have assumed a 1-to-1 mapping of all the positive integers to all the real numbers x, 0 < x < 1. They're all used up, both reals and integers. The construction of the diagonal number is clearly not equal to any number in the list - it is different in one position from each and every number listed.
It's not 'further down' because the assumption we started with that we have already mapped them all. Thus is derived a contradiction - we can't have mapped them all because the diagonal number is not in the list.

Skepticism is not a position; it is an approach to claims.
Science is not a subject, but a method.
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10-09-2012, 09:50 PM
RE: Math "Disproofs"
(10-09-2012 09:41 PM)Chas Wrote:  
(10-09-2012 07:18 PM)Starcrash Wrote:  If anyone has wondered where I've been for the past week...









Apparently mathematicians didn't stumble across this because they didn't realize that math with infinities was so simple.

Feel free to criticize.

I think your reflexive list is brilliant. However, it has nothing much to do with the proof.

The heart of a RAA proof is that something is assumed to be true and from this we derive a contradiction.

We have assumed a 1-to-1 mapping of all the positive integers to all the real numbers x, 0 < x < 1. They're all used up, both reals and integers. The construction of the diagonal number is clearly not equal to any number in the list - it is different in one position from each and every number listed.
It's not 'further down' because the assumption we started with that we have already mapped them all. Thus is derived a contradiction - we can't have mapped them all because the diagonal number is not in the list.

I know you just don't get this Cantor's diagonal thing, so let me spell it out for you. Whatever it produces is not a real number. The set that you want to add its product to contains all real numbers, and you're claiming that you made something that isn't on the list: hence, it's not a real number.

Also, Cantor's diagonal will never produce a number because that's how infinity works. Sure, it's an infinite line, but it's also passing through infinity. It's like flying through space. It doesn't matter if your flight path is infinite -- you'll never reach the edge because there isn't one. So you can't get to the end of the set to make a new number... because there isn't one.

And because I'm sure you still don't get it, consider if you did actually produce a number with that method. The number it matches? Easy... I'll just hand you back your number. Oh, you claim that you already passed through that number and changed a digit? Then even the diagonal number you made doesn't equal itself, because you'll change it every time you finish it. Trust me, the diagonal method is bullshit. It sounded like a clever thing, but it's fallacious on several levels.

My girlfriend is mad at me. Perhaps I shouldn't have tried cooking a stick in her non-stick pan.
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10-09-2012, 09:55 PM
RE: Math "Disproofs"
(10-09-2012 09:05 PM)Chas Wrote:  
(10-09-2012 07:18 PM)Starcrash Wrote:  If anyone has wondered where I've been for the past week...









Apparently mathematicians didn't stumble across this because they didn't realize that math with infinities was so simple.

Feel free to criticize.

1/9 = 0.1111...
2/9 = 0.2222...
3/9 = 0.3333...
4/9 = 0.4444...
5/9 = 0.5555...
6/9 = 0.6666...
7/9 = 0.7777...
8/9 = 0.8888...
9/9 = 0.9999...

No... 1/9 is .1111... with a remainder of .0...01. (Same all the way down through 8/9) I did the math, and you didn't pay attention. 9/9 certainly is 1, but that's because you've magically hit the point where the remainder becomes divisible and can be added in, so it no longer remains invisible. Algebra doesn't work the way you think it does. Try again.

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11-09-2012, 04:49 AM
RE: Math "Disproofs"
(10-09-2012 09:05 PM)Chas Wrote:  1/9 = 0.1111...
2/9 = 0.2222...
3/9 = 0.3333...
4/9 = 0.4444...
5/9 = 0.5555...
6/9 = 0.6666...
7/9 = 0.7777...
8/9 = 0.8888...
9/9 = 0.9999...

Consider this, too... If .9...99 = 1, then X - X = 0, right? 1 minus .9...99 = .0...01, and .9...99 minus 1 equals -.0...01. Just do the math.

1.00...000
.99...999
0.00....001

Also, X squared = X squared, right?
1 squared = 1.0...00
.999 squared = .99...981

Multiplication with infinite numbers can be hard, but even if you don't want to try doing the entire math equation for yourself, you'll notice immediately that it ends in 1, not zero.

The math doesn't work at all. And it's interesting that, after I blow away the math that you yourself used to prove this in our earlier debate, you resort to trying to prove it through pattern instead. It's a rounding error in your pattern, and in the equation. It always was and always will be.

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11-09-2012, 07:19 AM
RE: Math "Disproofs"
(11-09-2012 04:49 AM)Starcrash Wrote:  
(10-09-2012 09:05 PM)Chas Wrote:  1/9 = 0.1111...
2/9 = 0.2222...
3/9 = 0.3333...
4/9 = 0.4444...
5/9 = 0.5555...
6/9 = 0.6666...
7/9 = 0.7777...
8/9 = 0.8888...
9/9 = 0.9999...

Consider this, too... If .9...99 = 1, then X - X = 0, right? 1 minus .9...99 = .0...01, and .9...99 minus 1 equals -.0...01. Just do the math.

1.00...000
.99...999
0.00....001

Also, X squared = X squared, right?
1 squared = 1.0...00
.999 squared = .99...981

Multiplication with infinite numbers can be hard, but even if you don't want to try doing the entire math equation for yourself, you'll notice immediately that it ends in 1, not zero.

The math doesn't work at all. And it's interesting that, after I blow away the math that you yourself used to prove this in our earlier debate, you resort to trying to prove it through pattern instead. It's a rounding error in your pattern, and in the equation. It always was and always will be.

There is no rounding error. You are mistakenly terminating a non-terminating decimal expansion.

Skepticism is not a position; it is an approach to claims.
Science is not a subject, but a method.
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11-09-2012, 07:25 AM
RE: Math "Disproofs"
(10-09-2012 09:50 PM)Starcrash Wrote:  
(10-09-2012 09:41 PM)Chas Wrote:  I think your reflexive list is brilliant. However, it has nothing much to do with the proof.

The heart of a RAA proof is that something is assumed to be true and from this we derive a contradiction.

We have assumed a 1-to-1 mapping of all the positive integers to all the real numbers x, 0 < x < 1. They're all used up, both reals and integers. The construction of the diagonal number is clearly not equal to any number in the list - it is different in one position from each and every number listed.
It's not 'further down' because the assumption we started with that we have already mapped them all. Thus is derived a contradiction - we can't have mapped them all because the diagonal number is not in the list.

I know you just don't get this Cantor's diagonal thing, so let me spell it out for you. Whatever it produces is not a real number. The set that you want to add its product to contains all real numbers, and you're claiming that you made something that isn't on the list: hence, it's not a real number.

Also, Cantor's diagonal will never produce a number because that's how infinity works. Sure, it's an infinite line, but it's also passing through infinity. It's like flying through space. It doesn't matter if your flight path is infinite -- you'll never reach the edge because there isn't one. So you can't get to the end of the set to make a new number... because there isn't one.

And because I'm sure you still don't get it, consider if you did actually produce a number with that method. The number it matches? Easy... I'll just hand you back your number. Oh, you claim that you already passed through that number and changed a digit? Then even the diagonal number you made doesn't equal itself, because you'll change it every time you finish it. Trust me, the diagonal method is bullshit. It sounded like a clever thing, but it's fallacious on several levels.

I suggest you study up on infinite series and induction to aid your perception of countable infinity.

Also, you are still missing how a reductio ad absurdum proof works.

Skepticism is not a position; it is an approach to claims.
Science is not a subject, but a method.
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11-09-2012, 07:31 AM
RE: Math "Disproofs"
(10-09-2012 09:55 PM)Starcrash Wrote:  
(10-09-2012 09:05 PM)Chas Wrote:  1/9 = 0.1111...
2/9 = 0.2222...
3/9 = 0.3333...
4/9 = 0.4444...
5/9 = 0.5555...
6/9 = 0.6666...
7/9 = 0.7777...
8/9 = 0.8888...
9/9 = 0.9999...

No... 1/9 is .1111... with a remainder of .0...01. (Same all the way down through 8/9) I did the math, and you didn't pay attention. 9/9 certainly is 1, but that's because you've magically hit the point where the remainder becomes divisible and can be added in, so it no longer remains invisible. Algebra doesn't work the way you think it does. Try again.

There is no remainder. It is an infinite expansion, a power series.

Skepticism is not a position; it is an approach to claims.
Science is not a subject, but a method.
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11-09-2012, 12:55 PM
RE: Math "Disproofs"
Numbers of the form "0.000...0001" implying an infinite series of 0s followed by a one, do not exist. They are mathematically invalid. An infinite series cannot be terminated.

Read up on infinity and transfinities and how mathematics actually deals with the concept of infinity.

E 2 = (mc 2)2 + (pc )2
614C → 714N + e + ̅νe
2 K(s) + 2 H2O(l) → 2 KOH(aq) + H2 (g) + 196 kJ/mol
It works, bitches.
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