can 1 = 2?

Question

is there some type of trick in math

Answer 1

The (FALSE) proof that 1 = 2 goes as follows.

Let a = 1 and b = 1.

Then

a = b

If we square both sides of that equation, we get
a^2 = b^2

and if we multiply both sides of that same equation by a, we get

a^2 = ab

So we have these two equations:

a^2 = b^2
a^2 = ab

Let's rearrange both of these, to:

a^2 - b^2 = 0
a^2 - ab = 0

Since both of these equate to 0, they equate to each other.

a^2 - b^2 = a^2 - ab

Factor both sides, to obtain

(a - b) (a + b) = a(a - b)

Now that we have (a - b) on both sides, they effectively cancel out because we divide both sides by (a - b). As a result, we get

a + b = a

We initially assigned a = b = 1; therefore

1 + 1 = 1, and
2 = 1

This is a more elegant false proof than the one posted above because in the above example, value of "a" was equal to 1 at the start and then "became" 0 later. Here, the value of "a' remained consistent throughout.

Nevertheless, it's still a false proof.

Answer 2

Well, 1 cannot equal 2. However, if you are talking in terms of a graph (y = mx+b), it is possible for 1 to equal 2, but it is not the same thing. It actually means that y = 1 and x = 2.

Answer 3

well, people will say 1 is not equal to 2 but they will have a same thought that it is some kind of trick.

Answer 4

I dont know the trick but i know that 1=2 in calculus

Answer 5

To beach bum: While it's true that 1=2 proofs are BS, this is not the case for 1 = 0.999... This is in fact true and can be proven in various ways, all perfectly valid.

Show me a number that is less than 1 by any small amount, and I will show you a number that is less than 0.999...

Answer 6

Well, numbers are a creation of the human mind to explain the universe. Therefore numbers don't really exist and you could invent your own system in which 1=2.

Answer 7

1 definitely can equal .99999999999999...
1/3 = .333333...
3 * 1/3 = .333333... *3
1 = .999999999...

This next way is a bit less mathematic but here it goes
1/9 = .11111111111111...
2/9 = .22222222222222...
3/9 = .33333333333333...
4/9 = .44444444444444...
5/9 = .55555555555555...
8/9 = .88888888888888...
9/9 = .99999999999999...
9/9 = 1/1 = 1

Answer 8

1/n(1 +1 +1 +1 +1 +... + 1+1) = 2n( 1+ 1+1 +1+1 +1 +1 +...+1+1)

(1/n) (n) =( 2/n)( n) ( 1 repeated n times)

1 = 2

Answer 9

There are lots of "proofs" that 1 = 2, all bogus. Show us the one you have been given, and we'll be happy to point out the flaw in the logic. :)

Answer 10

on a graph, at a y value of 1, the x value may equal two, hence, 1 = 2. An example of this would be on the graph y=2x. The notation however would not be 1=2. to write it that way would be wrong.