# Prove that 1 + 1 is 1 with Formal Logic [closed]

Puzzle:

Prove that $1 + 1$ is $1$ using formal logic.

Hint:

$1 + 0$ is $0$

Hint 2 (edit):

No new definitions are required. The solution does have to do with the symbol + other actual (perhaps less formal) definitions.

• Howw can yu explain that with "formal logic" but tagged as lateral thinking? I just thought thays ironic, but you probably have your own explanation. Feb 17, 2018 at 15:18
• @North There is definitely a reason. It's what makes this puzzle work. Feb 17, 2018 at 15:19
• Given that you have to go outside normal mathematics, there are endlessly many different solutions, each one just as good as the other, and no way to tell which answer is the correct one.
– Bass
Feb 17, 2018 at 18:14
• I’m thinking this is more a coding question where + is more of an ‘and’ so 1 and 1 is true (1) and 1 and 0 is false (0) Feb 19, 2018 at 20:19
• @AggieKidd That's what I was thinking. And I used "formal logic" because and is an operation in formal logic. Feb 21, 2018 at 1:40

I suspect there will be multiple answers to this, but here's one:

Define the "+" operator to mean "the following number."

Then:

1 + 0 is 0
1 + 1 is 1

In fact,

x + 0 is 0, for any x, and x + 1 is 1, for any x, etc.

• Similar to my first thought. Formally define the + symbol as a multiplication operator. Feb 18, 2018 at 3:48
• @MattStevens that would also work - and it's perhaps simpler than mine :) Feb 18, 2018 at 6:41
• That's not exactly what I was thinking. No new definitions are required. The solution does have to do with the symbol + other actual (perhaps less formal) definitions. Feb 18, 2018 at 18:30