Mathematical Proof: 1 = 2 @ Sumeet’s Treasures

Mathematical Proof: 1 = 2

May 19th, 2006

My little brother is a math genius. I kid you not. He sent me an e-mail yesterday giving a very simple but - obviously - true proof that 1 equals 2. Here it is for your thinking pleasure:

a=x

Add `a` to both sides:

a + a = a + x

Combine like terms:

2a = a + x

Subtract `2x` from both sides:

2a - 2x = a +x - 2x

Combine like terms:

2a - 2x = a - x

Factor out a ‘2′ on the left and ‘1′ on the right:

2 (a-x) = 1 (a - x)

Divide both sides by `(a-x)`:

2=1

Voila!

Now, who can tell me why my brother is not only a mathematical genius, but also a joker?

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Entry Filed under: Gems, Thoughts, Geek Humor, Geeky, Family

10 Comments Add your own

1. Matt Conway | May 19th, 2006 at 2:45 pm

Your brother’s a joker because in the last step you divded by (a-x) which is division by 0, given that your first assumption is that a=x. Division by 0 is, of course, not defined, which means you basically void your warranty after that. Cute trick though.
2. Sumeet | May 19th, 2006 at 3:01 pm

Nicely done, Matt. It is a pretty fun trick, isn’t it?

It worries me, though, that my cousin (a rising Junior at UC Davis studying Economics) couldn’t figure it out. In her defense, though, she was eating pizza at the time.
3. Suneel | May 19th, 2006 at 5:24 pm

Uh, Sumeet, I didn’t make that up. It’s online somewhere. I just sent it to you because I thought it was a kind of interesting. Just clarifying that- don’t want to plagarize or anything.
4. Sumeet | May 19th, 2006 at 5:25 pm

I assumed as much, Suneel. But it’s a much more compelling post to phrase it this way. No dishonesty - just laying out the facts in a more dramatic fashion.
5. Arpan | May 20th, 2006 at 7:51 pm

Hmm… isn’t that what Bill O’Reilly does?
6. Austin | May 23rd, 2006 at 12:29 pm

well sorry to clarify but… dividing by 0 doesn’t mean this proff is wrong… actually because a=x then a-x or x-a both = 0 and ANYTHING times 0 =0 so by this same way you could ‘prove’ 400=3 ect.
7. Sumeet | May 24th, 2006 at 8:54 am

Arpan: I’ll not dignify that with a response.

Austin: Good catch! So the proof isn’t wrong! Suneel, you’re a genius. The next time I get asked a math question at a job interview, I’m totally gonna say, “Well, actually that’s not true… You see, four and seven are the same. Observe…” Yea, that’ll be awesome.
8. Mike | May 31st, 2006 at 3:29 pm

You cant factor on both sides.. because you have to factor out the same number for both sides
9. Sumeet | May 31st, 2006 at 11:01 pm

Hi Mike,

I think you’re confusing factoring out a value from a statement and dividing an equation by a number.

If we have a + b = c - d, then we certainly can’t just arbitrarily divide `a + b` by 2 and divide `c - d` by 1. But if we factor out a value from `a + b`, we’ll still arrive at `a + b` when we factor it back in.

Or at least that’s what I remember from another lifetime…
10. Mike | July 10th, 2006 at 9:59 am

Ahhh ive figured it out.

2(a-x)= 1(a-x)
Simplify this using distributive property.
2a-2x=1a-1x
Add 1x to both sides
2a-1x=1a
Once again, Add 1x to both sides.
2a=1a+1x
Subtract 1a
1a=1x
Which simplifys to a=x