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# Fun With Mathematics..proof Of 1=0

ravi_9793
Consider two non-zero numbers "a" and "b" such that
a = b.
Then aa= ab.
Subtract the same thing from both sides:
aa - bb = ab - bb.
Dividing by (a-b), we get
a + b= b.
Since a = b, we see that
2 b= b.
Dividing both sides by "b"
We get 2 = 1,
Subtracting 1 from both sides,
1 = 0.

Can you find what is wrong in this proof....
According to me...
a=b, so a-b=0 and we cannot divide by zero.
obviously there is something wrong in it but at the first sight it looks catchy...
Bondings
 ravi_9793 wrote: According to me... a=b, so a-b=0 and we cannot divide by zero.

Indeed, if you divide by zero, the whole equation becomes incorrect. It's nothing more complicated.
Aless
Yes, but to the uneducated eye, it looks spiffy and confusing.
Wynand
Here is a similar one. What is zero divided by Zero. Do you think it is Zero?

If you have nothing you actually have one.

X Divided by X is one,

So if X is zero then

Zero Divided by zero is one,

Therefore, if you have nothing and you give it to no – one you actually have one.

This is the reason that you cannot divide by zero. Not even zero by zero.
crdowner
There is a reason - how can you divide anything by nothing? What would be the point? Dividing by nothing would not accomplish anything.
nilsmo
http://en.wikipedia.org/wiki/Divide_by_zero
One way of defining a/0 if a isn't 0 is plus or minus infinity. 0/0... is it nullity? http://www.bbc.co.uk/berkshire/content/articles/2006/12/06/divide_zero_feature.shtml

Oh, and Wynand, there's many ways to say what 0/0 is:

1. Look at 0/x. As x gets closer to 0, the result goes towards 0.
2. Look at x/+0. As x gets closer to 0, it goes towards +infinity.
3. Look at x/-0. As x gets closer to 0, it goes towards -infinity.
4. As you said, look at x/x. As x goes to 0, it goes to 1.
william
For years, I've been trying to prove 1=2. In all cases I've had to divide by zero, which you can't.

Here's one of mine:

(x²-x²) = (x²-x²)

x(x-x) = (x+x)(x-x)

x = x+x

x= 2x

You basically can't divide by nothing.

But sometimes I wonder if it's only because the human mind can't understand "nothing." Is zero the opposite of infinity? What is nothing? All questions a human may ask but never answer.
a.Bird
 william wrote: For years, I've been trying to prove 1=2. In all cases I've had to divide by zero, which you can't. Here's one of mine: (x²-x²) = (x²-x²) x(x-x) = (x+x)(x-x) x = x+x x= 2x You basically can't divide by nothing. But sometimes I wonder if it's only because the human mind can't understand "nothing." Is zero the opposite of infinity? What is nothing? All questions a human may ask but never answer.

I'm almost positive that (x+x)(x-x) = 2x²-2x², not x²-x²
Bondings
 a.Bird wrote: I'm almost positive that (x+x)(x-x) = 2x²-2x², not x²-x²

They are both zero. And zero is almost positive.
skygaia
at first, it's very interesting...

a-b=0 so....

if you divide by zero, the whole equation becomes incorrect.
 Wynand wrote: Here is a similar one. What is zero divided by Zero. Do you think it is Zero? If you have nothing you actually have one. X Divided by X is one, So if X is zero then Zero Divided by zero is one, Therefore, if you have nothing and you give it to no – one you actually have one. This is the reason that you cannot divide by zero. Not even zero by zero.

My algebra teacher worked proved that equation on the board. Yes, it took the entire board to do it but she did in all of it's glorious logic.
ravi_9793
 william wrote: For years, I've been trying to prove 1=2. In all cases I've had to divide by zero, which you can't. Here's one of mine: (x²-x²) = (x²-x²) x(x-x) = (x+x)(x-x) x = x+x x= 2x You basically can't divide by nothing. But sometimes I wonder if it's only because the human mind can't understand "nothing." Is zero the opposite of infinity? What is nothing? All questions a human may ask but never answer.

this is also very interesting. ..wow. .I got another funny mathematical prove.
RhysAndrews
Mathematics doesn't always have to make perfect sense to even experts... to say there are no zeros in zero doesn't really make sense - but then, saying there is ONE zero in zero does make sense... it's just 1X0, thus, 0 doesn't have to equal 1. Just... 0 = 1X0.

-Rhys
Vrythramax
I don't know why Bondings didn't lock this topic....but if he didn't...neither will I....but it all seems like bunk to me.

Get a dog or a cat....they can be quite fetching.
Rako
I got a smiler question on a 9th grade math test i guess last year. so i don't think it is that hard it should be easy for most of you.