This is referred to as a chestnut but it amuses me.

x = 1

Therefore: x² = x

x² - 1 = x -1

Factorising x² - 1 we get

(x - 1)(x + 1) = x - 1

Dividing both sides by (x - 1) we get:

x + 1 = 1


Substituting 1 for x we get:

2 = 1

I LEARND THAt in class yesterday

every stupid person knows 2 doesnt equal one.

if x=1, and u devide by x-1, then x-1=1-1=0

DIVisION BY ZERO!!!!!!!!! not allowed

fallacious

hmmmmmmmmmm.......fun yes, but misleading isn't it?

this is how i see it:

x = ?

Therefore: x² = (x)(x)

x² - 1 = (x)(x)-1

Factorising x² - 1 we get

(x - 1)(x + 1) = (x)(x)-1

Dividing both sides by (x - 1) we get:

(x - 1)(x + 1) / (x-1) = (x)(x)-1 / (x-1)


Substituting 1 for x we get:

0 = 0

I'm not a math student, so I wanna know, if your factorising numbers can produce a multiplication by zero is it not faulty math?

just curious.

heres another one for you

this is how .999 = 1


.999 divided by 3 = .333

.333 = 1/3

1/3 x 3 =1

hows that work out?

well,

0.99999... does = 1

what is 1 - 0.99999999... =?

It equals 0.0000...(infinite 0s)...001 right?

Well, if you have infinite zeros,

0.0000...(infinite 0s)...001 = 0

So
.99999... = 1

Obviously .333 doesn't equal 1/3. Rounding error.

Sandy

Here's a few stolen from the net:

x^2 = x + x + . . . + x (With x terms on the right, x^2 = x * x.)
2 x = 1 + 1 + . . . + 1 (Take the derivative of each side.)
2 x = x (We added up the x 1's on the right.)
2 = 1 (Divide both sides by x.)

-------------------------------------------------------------

Whoever Knows the Least Earns the Most (the Dilbert Equation)

Engineers and scientists can never earn as much as business execs and sales reps. This can be supported by a mathematical theorem based on two postulates:

P1: Knowledge is Power
P2: Time is Money.

Basic physics definition: Power = Work / Time
Substituting the postulates, Knowledge = Work / Money
A little algebra gives us: Money = Work / Knowledge
Now as Knowledge --> 0 , Money --> oo (infinity).
So for any amount of work: Whoever knows the least earns the most!

Sandy

____
.999

____
.333

thats what i ment. bars over the # mean that it infinate #s

_
0.9 = 1

It may be some kind confusing in the first place but I asked my math professor this question two years ago and according to my memory the answer was:
They are two different writings for the same number. They are the same because you can not name a number which is greater than the first and lower than the last. And that is a condition for different real numbers.
So Adam is right.

Andreas

i just learned that too haha

Here's another way to really prove that 0.99999..... is EXACTLY equal to 1 :

set x=0.999999.....

then by multiplying both sides by 10:

10x=9.999999.....

subtracting the equations from one another:

10x=9.999999.....
- x=0.999999.....
---------------------
9x=9

simplifying:

x=1

so x=0.9999999.....=1 EXACTLY!!!

They way I learned that was

1/9 = .11111111111 unending

+8/9 = .88888888888 unending

___
9/9 = .99999999999 unending = 1

but you can see what's happening with 1 - 0.99999999999 unending = 0, because one minus .9 would be .1, but you don't get that because 1 minus .09 = .01 but you don't get that because of because 1 minus .009 = .001 and so forth. You never get to that .000000whatever1 because you never run out of nines.

Infinites are interesting things.

I have a calculator which gives an error if I try to take the square root of zero or a negative number, but gives the answer 1 for the square root of negative zero!

David J

if only we can take this information and turn it into money and find a way to get $.01 for every dollar and do it 10,000,000 times then we would be millionaires.

Didn't Richard Pryor do that in Superman III?

Yes, they also did it in Office Space, asking if it was done in Superman III.

Anyways, I had a professor in college that said most of the 0 = 1 proofs always had a divide by zero somewhere in them. Also, infinity is a concept, not a number.

A more interesting proof we did was actually proving that if you multiply 9 by any number add recursively add the digits, you'll get 9. And then we expaned on it and shows that for any base n, if you multiply by (n-1) and recursively add, you'll get (n-1).

haha i remmber that, i watched it again a couple nights ago

That's pretty interesting. I never would have thought of that. It certainly holds true for the built-in base 2, 8 and 16 features on the Windows calculator, as long as you don't multiply n-1 by 0, that is.

Sandy