does anyone know how to do this? my teacher said that she can prove it, she said that in ceartain instances, numbers may be forced to do things that they are not supposed to do....

 

alternatively, does anyone have any other simple problems like this that you could prove like 1+5=5 or something

 

seriously, any ideas at all, no matter how absurd OR complex, would be appreciated

I can prove that 2 = 1.

 

Let's assume that we have two numbers, a and b, and a = b.

 

We can see that

 

[math]a^2 = a \times b[/math]

 

because a = b.

 

Subtracting b² from both sides...

 

[math]a^2 - b^2 = ab - b^2[/math]

 

and then factoring:

 

[math](a + b)(a - b) = b(a - b)[/math]

 

There's an (a - b) on both sides, so it can be canceled out, leaving

 

[math]a + b = b[/math]

 

Because a = b:

 

[math]b + b = b[/math]

 

[math]2b = b[/math]

 

Divide by b:

 

[math]2 = 1[/math]

 

There is, of course, an error, but it's tough to find.

 

[hide]You can't cancel out (a - b). To cancel out, you have to divide by (a - b) -- and (a - b) = 0. Dividing by zero isn't allowed.[/hide]

Hopefully you know that √(-1)=i

 

Therefore:

1 + 1

= 1 + √1

= 1 + √(-1*-1)

 

[as you know √(ab) = √a√b]

 

= 1 + √(-1)√(-1)

= 1 + i*i

 

[as √(-1)=i, i²=-1]

 

= 1 - 1

= 0

 

Thus 1+1=0. QED.

 

Of course like always there's a flaw in it.

 

Now I've shown off the one I know(!), here's a good link:

http://en.wikipedia.org/wiki/Invalid_proof

also Google searches will give you more, if you want.

I can prove that 2 = 1.

 

Let's assume that we have two numbers, a and b, and a = b.

 

We can see that

 

[math]a^2 = a \times b[/math]

 

because a = b.

 

Subtracting b² from both sides...

 

[math]a^2 - b^2 = ab - b^2[/math]

 

and then factoring:

 

[math](a + b)(a - b) = b(a - b)[/math]

 

There's an (a - b) on both sides, so it can be canceled out, leaving

 

[math]a + b = b[/math]

 

Because a = b:

 

[math]b + b = b[/math]

 

[math]2b = b[/math]

 

Divide by b:

 

[math]2 = 1[/math]

 

There is, of course, an error, but it's tough to find.

 

[hide]You can't cancel out (a - b). To cancel out, you have to divide by (a - b) -- and (a - b) = 0. Dividing by zero isn't allowed.[/hide]

 

If a and b have exactly the same value, then why bother using two different letters for it?

 

Does that sequence of equations still work if you only use one letter?

It's more obvious what the problem is if you use one letter, and hence people notice more quickly.

cool thanks

 

any others??

`+` is frequently use to represent OR.

if you look at the Truth Table for an OR gate you`ll see that 1+1 is True or 1

(unless it`s an XOR).

I thought "^" was OR?

`V` Is using Formal logic symbology.

 

but `+` and `.` are also used to represent OR and AND respectively.

 

here: http://hyperphysics.phy-astr.gsu.edu/Hbase/electronic/diglog.html

and here: http://www.asic-world.com/digital/boolean1.html#Function_Definitions