1 + 1 = 2

[u2205]

So I got asked a question earlier on these forums to prove that 1+1=2 and I think this is a correct proof and I was wondering if there was any other math buffs here who could check it for me.

Thanks!

The proof starts from the Peano Postulates, which define the natural
numbers N. N is the smallest set satisfying these postulates:
  1)  1 is in N.
  2)  If x is in N, then its "successor" x' is in N.
  3)  There is no x such that x' = 1.
  4)  If x isn't 1, then there is a y in N such that y' = x.
  5)  If S is a subset of N, 1 is in S, and the implication
       (x in S => x' in S) holds, then S = N.

Then you have to define addition recursively:
  Def: Let a and b be in N. If b = 1, then define a + b = a'
       (using P1 and P2). If b isn't 1, then let c' = b, with c in N
       (using P4), and define a + b = (a + c)'.

Then you have to define 2:
  Def:  2 = 1'

Theorem:  1 + 1 = 2

Proof: Use the first part of the definition of + with a = b = 1.
       Then 1 + 1 = 1' = 2  Q.E.D.

[DancingTofu]

Looks kosher.  Good job.

[NightLotus]

discrete maths make my brain bleed ><

[TanisNikana]

It's not kosher.

It's all really fancy math up until you get to the proof proper, when Mustash goes 1 + 1 = 1'. Here we can assume that 1' = 2 because of P1 and P2, because x' = x + 1. In the proof, we then have the phrase "1 + 1 = 2 = 2". This is math for "because I said so", and while it's correct and we can all validate it, "because I said so" is not a good answer for a proof.

The catch about this is that 1 + 1 = 2 cannot properly be proved with addition, recursive or not. Is like someone saying "God is almighty because he wrote the bible, which says he's almighty". Need to prove it with something else.

I prefer proving it with coconuts, one in each hand. That makes two coconuts.

[TanisNikana]

And:

http://mathforum.org/library/drmath/view/51551.html
http://www.physicsforums.com/showthread.php?t=55334

[melchizedek]

You are a freshman Patrick, you shouldn't be having to do more than read over proofs until you get into junior level math

[TomtheFanboy]

For extremely dull values of 1.

[TanisNikana]

And:

http://mathforum.org/library/drmath/view/51551.html
http://www.physicsforums.com/showthread.php?t=55334

Yes I did get help from these sites for formatting. I do have this proof written in my Discrete Lab book from two weeks ago but it uses all sorts of funny "Union", "Intersection", "Exists", and "Apples to all" signs in it and I didn't know how to type if out for the computer.

Not saying you plagiarized, just adding more references.

[superjaz]

k but can you explain to me how 6 is greater then 8?

 

[TanisNikana]

k but can you explain to me how 6 is greater then 8?

 

It's not. No two ways about it.

[superjaz]

k but can you explain to me how 6 is greater then 8?

It's not. No two ways about it.

 thats what i said but the customer service lady at safe way got frustrated at me when i tried to tell her otherwise and she said"let me find some one to explain it to you in a way you'll under stand

[Blackstar]

I have no clue what you are saying patrick but OK 

[dshwshr55]

They're just trying to decide who's the buffest mathematician.

I prefer proving it with coconuts, one in each hand. That makes two coconuts.

I prefer the visual aid more than the numbers when it comes to math.
Two coconuts! Not 1 1/2, not 3...

[dshwshr55]

Yes, but a different species of coconut is still a coconut.
A square is a rectangle, but a rectangle is not a square.

[TanisNikana]

k but can you explain to me how 6 is greater then 8?

It's not. No two ways about it.

 thats what i said but the customer service lady at safe way got frustrated at me when i tried to tell her otherwise and she said"let me find some one to explain it to you in a way you'll under stand

This is because customers are often wrong. You'd be surprised how many people honestly think 1 and 1 is 11. (Hint: greater than 15% of Americans...)

[dshwshr55]

So next Kumoricon, I can ask 100 people what 1+1 equals, and more than 15 of them will say 11?

[soundninja12]

woah...
I didn't know anyone could make 1+1 complicated...

[TanisNikana]

So next Kumoricon, I can ask 100 people what 1+1 equals, and more than 15 of them will say 11?

Didn't say Kumoricon, I said Americans. Try asking in your local Walmart.

[soundninja12]

So next Kumoricon, I can ask 100 people what 1+1 equals, and more than 15 of them will say 11?

Didn't say Kumoricon, I said Americans. Try asking in your local Walmart.

c'mon, us anime nerds are smart...ish. I guess only like 5 will say 11 (one of which will be me,because now I know you're going to ask... and I must sabotage it... bwahahaha).

[soundninja12]

*dies a little bit inside*

[DancingTofu]

k but can you explain to me how 6 is greater then 8?

It's not. No two ways about it.

 thats what i said but the customer service lady at safe way got frustrated at me when i tried to tell her otherwise and she said"let me find some one to explain it to you in a way you'll under stand

Was she upside down?

[TanisNikana]

k but can you explain to me how 6 is greater then 8?

It's not. No two ways about it.

 thats what i said but the customer service lady at safe way got frustrated at me when i tried to tell her otherwise and she said"let me find some one to explain it to you in a way you'll under stand

Was she upside down?

I had to stare at that a few minutes before I figured it out.

[dshwshr55]

So next Kumoricon, I can ask 100 people what 1+1 equals, and more than 15 of them will say 11?

Didn't say Kumoricon, I said Americans. Try asking in your local Walmart.

c'mon, us anime nerds are smart...ish. I guess only like 5 will say 11 (one of which will be me,because now I know you're going to ask... and I must sabotage it... bwahahaha).

Well then, what if I ask 100 cosplayers instead?

[dshwshr55]

Do you have the figures?

[NightLotus]

i am still confused... just beeteedub ;;>_>

[NightLotus]

yup!! i is not crazy CS major like silly Patrick!
*cuddles* :3