Why is 2=1 wrong

And what's the big ruse that the sneaky number zero is attempting to pull off? Keep on reading to find out!. I know this sounds crazy, but if you follow the logic and don't already know the trick , I think you'll find that the "proof" is pretty convincing.

If you're not sure how FOIL or factoring works, don't worry—you can check that this all works by multiplying everything out to see that it matches. Everything we did there looked totally reasonable. What Are Mathematical Fallacies?

Which, good news, means you can relax—we haven't shattered all that you know and love about math. Somewhere buried in that "proof" is a mistake.

Actually, "mistake" isn't the right word because it wasn't an error in how we did the arithmetic manipulations, it was a much more subtle kind of whoopsie-daisy known as a "mathematical fallacy.

What was the fallacy in the famous faux proof we looked at? Like many other mathematical fallacies, our proof relies upon the subtle trick of dividing by zero. And I say subtle because this proof is structured in such a way that you might never even notice that division by zero is happening. Where does it occur?

Take a minute and see if you can figure it out… OK, got it? It happened when we divided both sides by a - b in the fifth step. But, you say, that's not dividing by zero—it's dividing by a - b. That's true, but we started with the assumption that a is equal to b , which means that a - b is the same thing as zero! And while it's perfectly fine to divide both sides of an equation by the same expression, it's not fine to do that if the expression is zero.

Because, as we've been taught forever, it's never OK to divide by zero! Which might get you wondering: Why exactly is it that we can't divide by zero?

We've all been warned about such things since we were little lads and ladies, but have you ever stopped to think about why division by zero is such an offensive thing to do?

There are many ways to think about this. We'll talk about two reasons today. The first has to do with how division is related to multiplication. Let's imagine for a second that division by zero is fine and dandy. We don't know what it is, but we'll just assume that x is some number.

We can also look at this division problem as a multiplication problem asking what number, x , do we have to multiply by 0 to get 10? Of course, there's no answer to this question since every number multiplied by zero is zero. Which means the operation of dividing by zero is what's dubbed "undefined. In other words, as we divide 1 by increasingly small numbers—which are closer and closer to zero—we get a larger and larger result. Connect and share knowledge within a single location that is structured and easy to search.

The operation would be acceptable in an example such as:. So completely valid. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more.

Asked 8 years, 5 months ago. Active 8 years, 5 months ago. Viewed 5k times. Community Bot 1. Red Banana Red Banana 22k 17 17 gold badges 78 78 silver badges bronze badges. I've even created a name for these guys. I would tend to agree One question is okay, two is pushing it, and certainly I will vote to close question number three Show 2 more comments. Active Oldest Votes.

Hope this clarifies more!