1=0???

JC 2K3

Ok you might have seen this before, but it's crazy, I think it's disproved by the fact that we can't divide by 0 or something.....

1^1=1
1^0=1

therefore 1=0

.....

Someone disprove this quickly, before I go crazy!

Sandals

But one is zero my child.

JC 2K3

JC 2K3 wrote:

1^1=1
1^0=1

therefore 1=0

How does that prove that 1=0? You have the powers being equal, not the numbers, i.e

1^15=1
1^997=1

doesn't mean that 15=997.

Tar.Aldarion

1. a = b + 1...... ............................................. 1. Given
2. (a-b)a = (a-b)(b+1)..... .................................2. Multiplication Prop. of =
3. a2 - ab = ab + a - b2 - b...... .........................3. Distributive Propoerty
4. a2 - ab -a = ab + a -a - b2 - b ...... ................4. Subtraction Prop. of =
5. a(a - b - 1) = b(a - b - 1) ...... .......................5. Distributive Property
6. a = b ...... ...................................................6. Division Property of =
7. b + 1 = b ..... ...............................................7.Transitive Property of = (Steps 1, 7)
8. Therefore, 1 = 0.............................................[QED]

Tar.Aldarion

2 is also = 0 of course!



Given that a and b are integers such that a = b, Prove: 0 = 2

1. a = b ............................................1. Given
2. a - b - 2 = a - b - 2 ........................2. Reflexive Prop. of =
3. a(a - b - 2) = b(a - b - 2) ................3. Multiplication Prop. of =
4. a2 - ab - 2a = ab - b2 - 2b ..............4. Distributive Propoerty
5. a2 - ab = ab - b2 - 2b + 2a ..............5. Addition Property of =
6. a2 - ab = ab + 2a - b2 - 2b ..............6. Associative Property of +
7. a(a - b) = a(b + 2) - b(b + 2) ...........7. Distributive Property
8. a(a - b) = (a - b)(b + 2) ..................8. Distributive Property
9. a = b + 2 ......................................9. Division Property of =
10. b = b + 2 ...................................10. Transitive Property (steps 1, 9)
11. Thereforem 0 = 2 ........................11. Subtraction Property of =

Sandals

Tar, is 3 equal to zero?

Tar.Aldarion

That wouldn't make sense now would it?

Capt'n Midnight

JC 2K3 wrote:

Ok you might have seen this before, but it's crazy, I think it's disproved by the fact that we can't divide by 0 or something.....

1^1=1
1^0=1

therefore 1=0

Now lets look at the case of N+1

(N+1)^0 =1

Hence,by induction all positive integers are the same.

Next week we will investigate the rational numbers.

smiles

JC 2K3 wrote:

Ok you might have seen this before, but it's crazy, I think it's disproved by the fact that we can't divide by 0 or something.....

1^1=1
1^0=1

therefore 1=0

.....

Someone disprove this quickly, before I go crazy!

Ok.

ln(1^1) = ln(1^0)
1*ln(1) = 0*ln(1)

ln(1) = 0.
Thus the inability of division by 0, so you cannot cancel the ln(1) on both sides.

Happy?

smiles

Tar.Aldarion wrote:

1. a = b + 1...... ............................................. 1. Given
2. (a-b)a = (a-b)(b+1)..... .................................2. Multiplication Prop. of =
3. a2 - ab = ab + a - b2 - b...... .........................3. Distributive Propoerty
4. a2 - ab -a = ab + a -a - b2 - b ...... ................4. Subtraction Prop. of =
5. a(a - b - 1) = b(a - b - 1) ...... .......................5. Distributive Property
6. a = b ...... ...................................................6. Division Property of =
7. b + 1 = b ..... ...............................................7.Transitive Property of = (Steps 1, 7)
8. Therefore, 1 = 0.............................................[QED]

Similar argument here.
We were told a = b + 1. So (a - b - 1) = 0

So to get from line 5 to line 6 you are dividing by 0.

(in the other one he posted division by 0 also line 8 to 9)

Sandals

You can't divide by zero though.

Crumbs

Sandals wrote:

You can't divide by zero though.

But zero = one and you can divide by one, so you can divide by zero.

FACT.

Sandals

Nonsense

JC 2K3

Deleted User wrote:

How does that prove that 1=0? You have the powers being equal, not the numbers, i.e

1^15=1
1^997=1

doesn't mean that 15=997.

hmm... 1 seems to be a special case when it come to powers, for instance you can say:

2^x=4
2^2y=4
2^x=2^2y
x=2y

but you can't say:

1^x=1
1^2y=1
1^x=1^2y
x=2y
?

Ok.

ln(1^1) = ln(1^0)
1*ln(1) = 0*ln(1)

ln(1) = 0.
Thus the inability of division by 0, so you cannot cancel the ln(1) on both sides.

Happy?

Thank you

---

btw

2-2=1-1=0
2(1-1)=1-1=0
2=1=0

of course you can't actually do that, since you can't divide by (1-1), but it's funny anyway

Tar.Aldarion

smiles wrote:

Similar argument here.
We were told a = b + 1. So (a - b - 1) = 0

So to get from line 5 to line 6 you are dividing by 0.

(in the other one he posted division by 0 also line 8 to 9)

Of course smiles, I didn't think I had gone and proven 1=0 and 2=0 when I am a second year engineer now did I.
Give me a year or two.

smiles

Sandals wrote:

You can't divide by zero though.

That was the point. ie. the error in the arguments.

Tar.Aldarion --> I was explaining to the guy who asked the question originally! You seemed to know exactly what you were doing.

Tar.Aldarion

I know, I know, just pulling your leg.

Chucky

Sandals wrote:

You can't divide by zero though.

But to get from line 5 to line 6 all you need do is divide both sides by (a - b - 1) and then it still works out as a=b. This example has intrigued me but I think it just goes to show that maths is not precise. Nothing really is now is it?


Edit: Although, I can now see why you can deduce that he was dividing by zero. The fact then that he divided by zero would suggest to me that the original equation of a = b + 1 cannot be true as it ends up undefined by maths.

David19

There's nothing wrong with stating a = b + 1. There is something wrong with dividing by zero though. Its only when he divided by a - b - 1 that the maths became wrong.

DingChavez

I hate maths.............

At least it's not Arts.

Tar.Aldarion

David19 wrote:

There's nothing wrong with stating a = b + 1. There is something wrong with dividing by zero though. Its only when he divided by a - b - 1 that the maths became wrong.

Ye chucky, stating a=b+1 makes perfect sense,
The more I think about samples that I write the more confused I become so I'll just say, you can't divide by 0...hmm or can I...
/whips out notepad.

Chucky

Haha, yeh ye are right. So, if you don't perform the illegal divide by zero (a - b - 1) then there is no way of solving this equation without further information. You'd need a simultaneous equation with it or a simple value for 'a' or 'b' would be nice!

spooner_j

Heres another one to think about:

Proof that 1=-1:

i =
so start with
i = i
or
=

Then since -1 = 1/(-1) or (-1)/1
=

square root of (a/b) = (square root of a) / (square root of b) so

-- = --


Cross multiplying gives
x = x

And so
1 = -1

QED!

Chucky

Masel-Tov! Quite cool

Gotta love them.

Theorem
1 + 2 + 4 + 8 + 16 + ... = -1

Proof:
Let x = 1 + 2 + 4 + 8 + 16 + ...

=> 2x = 2 + 4 + 8 + 16 + ...

---

x = -1 QED

smiles

Deleted User wrote:

Gotta love them.

Theorem
1 + 2 + 4 + 8 + 16 + ... = -1

Proof:
Let x = 1 + 2 + 4 + 8 + 16 + ...

=> 2x = 2 + 4 + 8 + 16 + ...

---

x = -1 QED

Now we're getting into infinities!
infinity - infinity is non-defined.

hence x - 2x is non-defined.

Fio

smiles

spooner_j wrote:

Heres another one to think about:

Proof that 1=-1:

i =
so start with
i = i
or
=

Then since -1 = 1/(-1) or (-1)/1
=

square root of (a/b) = (square root of a) / (square root of b) so

-- = --


Cross multiplying gives
x = x

And so
1 = -1

QED!

Why this one is out?
sqrt(a/b) = + or - sqrt(a) / sqrt(b)
It is only necessarily positive if both a and b are positive, which in this case they aren't.

This is a "disguised" version of:
1 = -1.-1
1 = sqrt(1) = sqrt(-1).sqrt(-1) = i.i = -1

Fio

bazpaul

spooner_j wrote:

Heres another one to think about:

Proof that 1=-1:

i =
so start with
i = i
or
=

Then since -1 = 1/(-1) or (-1)/1
=

square root of (a/b) = (square root of a) / (square root of b) so

-- = --


Cross multiplying gives
x = x

And so
1 = -1

QED!

lookin at the first rules on this page;

http://www.algebra-online.com/multiplying-dividing-square-roots-4.htm

it would appear that ur maths was wrong
sqr(-1)*sqr(-1)=sqr(-1*-1)=sqr(1)=1

smiles

smiles wrote:

Now we're getting into infinities!
infinity - infinity is non-defined.

hence x - 2x is non-defined.

Fio

Infinity equals 17.