True or False: 1 = 2?

Question

Are you sure?

Consider this:

a doesn't = 0 and is a positive number

1) a = b
2) ab = b^2
3) ab - a^2 = b^2 - a^2
4) a (b-a) = (b+a) (b-a)
5) a = b+a
6) a = 2 a
7) 1 = 2

Are you still sure?

Answer 1

you divided by zero....

when you divide by zero you go to hell

(b-a) = 0 and canceling is same as dividing by

Answer 2

Yes, I'm sure. 1 = 1 and 2 = 2, and 1 ≠ 2.

Here's a recent Best Answer to "I once saw a method of proving tht 2=1 It started a=b therfore ab= a "squared" Does anyone know the rest??"
http://answers.yahoo.com/question/index;_ylt=AsJxNgJXr90XlyQso0qSZT_sy6IX?qid=20060626065831AAYIBJi

You can't cancel (in step 5) because you're dividing both sides by zero, a math no-no.

Answer 3

False

1•0=2•0 (this is line 4) does not mean that 1=2 (line 5), you can not cancel the 0 (or a-b, as you have it written) because 0 has no inverse.

Answer 4

In step 4 you are diving by 0 (a-b) so therefore the whole thing goes out the window. Divide anything by 0 and it's undefined, or infinity; in either event, it doesn't prove 1=2. Sorry.

Answer 5

interesting.

after looking at this, i can see that a problem arises in step 3.

assuming that a = 1 during this step would mean (1x1) - (1^2) which would equal zero. Anything you do to zero will give you zero, for instance, you can multiply one side by a million and the other side by a billion and they will still equal zero.

math is quite fascinating though. =)

Answer 6

Step 4-5 is incorrect. Simplifying a(b-a) = (b+a)(b-a) gives you

ab = b^2, not a = b+a

Answer 7

when you cancelled (b-a), you divided by 0 (you started with a=b ===> b-a=0 ). This will give you an undefined answer, which makes your proof erroneous.

Answer 8

Keep at it. Who knows, maybe you will find the solution to the universe some day!

Answer 9

1 (body) = 2 (two legs)
you are right :))

Answer 10

Actually, it is true, it just doesn't work very well in this dimention.