1+1= not 2?

[bored_teen]

this info is from my dad:

my uncle is a math major. he used to explain to my dad how 1+1 does not equal 2. he would go through the steps, but my dad would never see any twist.

 

my uncle lives in california, and i don't feel like calling him in the middle of the night to ask him. so how does 1+1 not equal 2?????

[Daecon]

When it makes "11"?

[timo]

Try a search for "division by zero" on the math subforums. Should at least give similar tricks.

[the tree]

In terms of painfully pedantic axiomatic maths/logic, the definition of 2 is often 1+1. If you're using your definitions properly you wont come across contradictions like that.

 

Trans, when does it equal 11? Base-1?

[YT2095]

the "+" can also be the Boolean operator OR in which case 1+1=1

except in the case of XOR then 1+1=0

[the tree]

Really all the definitions are arbitrary and don't really mean anything, I suppose you could argue that 1+1=2 isn't true on the basis that it is just made up.

[YT2095]

I was actually being serious, "+" does indeed mean OR, as "." equals AND in Boolean algebra

 

it wasn`t arbitrary

[the tree]

I know. It is arbitrary though, in that '+' can mean addition or OR or whatever you need it to mean at the time. And there's no real reason to use + over §.

 

You create definitions and axioms in the hope that they create good maths, any definition that you use is as made up as the next.

[YT2095]

well there is unless you want to get Really silly 9I don`t think the OP wanted that), take a look here: http://en.wikipedia.org/wiki/Logic_gate

 

note also that "+" can be replaced by "V" if using Formal Logic operators instead.

 

so that squiggle thing you used is incorrect it`s V, and something like "/\" for AND.

 

trust me, I do this stuff in my sleep

[the tree]

Why is the squiggle thing incorrect? It will mean what I want it to mean, sure it's fairly non-standard notation but that's my point, the way you write stuff down doesn't add anything to what you're actually talking about.

[YT2095]

it does if you want to be Understood by the Rest of the population.

[the tree]

Does that change the fact that all definitions and axioms are as made up and arbitrary as the rules of any other game?

[YT2095]

it does if you want to be Understood by the Rest of the population.

 

as I said, and in your instance if you want to play the "game", then yes it does matter.

[the tree]

Mattering doesn't stop something from being made up and arbitrary. For instance, it is incredibly important that everyone drives on the same side of the road, but this is chosen arbitrarily.

[YT2095]

that may or may not be the case, how does this help the OP in anyway though? Thats the bit I still can`t get my head around

[the tree]

I think it was helpful up until around Post 6.

These helpful points have been made so far:

1. In base 1, 1+1=11
   
2. Definitions are essentially made up, 1+1 doesn't have to =2 if you don't want it to. However the commonly accepted definition is that 1+1=2.
   
3. There are plenty of erroneous proofs that come up with seemingly irrational contradictions, a search for "divide by zero" will help you find them. This is probably what the OP was looking for.
   
4. In logic, the '+' symbol means something different to what you are used to it meaning.
   

The rest was just me being terribly pedantic and you encouraging me.

[Daecon]

Trans, when does it equal 11? Base-1?

 

No, when you write two 1's on a piece of paper.

[the tree]

That wouldn't really fit with any regularly used definition of '+' then would it?

[YT2095]

if read Literally in Logic "1+1= not 2" is perfectly True!

 

let me explain, 1+1= 1V1

 

not 2 = ¬2

 

2 = 10 therefore not 2 (¬10) = 01

 

now read the original, 1V1=¬10

 

boiled down it`s: 1V1=1

 

That`s the bottom line

[the tree]

Yes yes, we get that you do logic, do keep it to yourself though.

[YT2095]

Pardon!?

 

I was actually addressing the Question as outlined by the OP, if that offends you in any way TUFF

[Daecon]

What about if you count backwards?

 

Then 1+1=0.

[Royston]

What about if you count backwards?

 

Then 1+1=0.

 

What ?

[the tree]

...

 

...

 

That was a slightly odd example of my original point.

[YT2095]

Then 1+1=0.

 

would be valid for:NAND ¬/\ also XOR (+)