1 + 1 = 1

Name: stephanie

Who is asking: Other Level: All

Question: Explain useing a proof of some form the propostion 1 + 1 = 1

My friend has this as a bonus question the other day and I want to figure it out. I don't know how 1+1 in any form could equal 1. Please let me know how you come about geting that. Thank you very much.

Hi Stephanie,

Hmmm, "A proof of some form..." The only kind of proof which would give you 1 + 1 = 1 would be a proof with a mistake in it (that is, an erroneous proof), because we all know that 1 + 1 = 2, so anybody trying to prove that 1 + 1 equals 1 would have to use some kind of deception to get there.

There are plenty of ways to make it appear that 1 = 2. Some use only simple algebra, others use complex analysis, or calculus or infinite series. Here is a simple way using algebra:

Suppose that we put x = 1 and y = 1. Then we have x = x² = 1 and y = y² = 1, so that

x² - y² = x - y. We can then factor the left side: (x + y)(x - y) = x - y

^{(x + y)(x - y)}/_{(x - y)} = ^{(x - y)}/_{(x - y)}

(x + y) = 1. Then, we can replace x and y by their values of 1, to get 1 + 1 = 1. Do you see what is wrong with that proof?

Cheers,
Claude Go to Math Central