Anything = Anything?

[Cheddar]

My friend says he's found a way to prove any number equals any other number... I know it can be disproven, because in actuality it isn't true, but it's a bit interesting how he came up with this.

Take 3 = 4... we need to turn this into a true statement.

So my friend multiplies both sides by 0, and by definition, that keeps both sides equal.

So 0 = 0, a true statement.

Of course, this appears to work with any two numbers, but I'm having a hard time with it... you should start with a true statement, right?

Even though it's a simple trick, it's true in theory.

I so want to use this on a math test someday.

 

[SilverHawk]

Multiplying both sides by zero is actually not a legal move when solving an equation, for the reason your friend pointed out.

 

[esb]

So basically it's

0+0+0=0+0+0+0

NOT 3=4
It's Three Zeroes equal Four Zeroes.

 

[enouwee]

I so want to use this on a math test someday.

Test, which you fill fail miserably.

As for the "proof":
3 = 4
<=> 3 * x = 4 * x | x > 0
<=> 4 * x = 3 * x
<=> (4 - 3) * x = 0
<=> 1 * x = 0
<=> x = 0

Which "confirms" the zero element property of the multiplication.