1 + 1 = 2 without adding?

[bigyihsuan]

Is it possible to do 1+1=2 without adding?

[rryy]

1-(-1)=2

Does that count?

[swiftgates24]

No. 1 + 1 = 2 Can never be changed, because it is already itself 1 - ( -1 ) = 2 does get 2, but it is not 1 + 1 = 2

1 + 1 = 2 without adding is 1 1 = 2, which isn't valid because there is no operation before the equal sign.

[Nuke]

1<<1=2

lol.

i like programming in cpu arcitectures that do not have hardware multiply. and this right shift by 1 is equivalent to multiplication by 2. essential operations when dealing with bit fields, also useful for implementing binary fixed point numbers. you shift the integer part and then or in the fractional. that said you could also do this:

1*2=2

Edited May 18, 2013 by Nuke

[bigyihsuan]

I said without adding. Technically, multiplication and division use adding (multiply = repeated addition, division = multiply to find second number to subtract).

[ROFLCopter64bit]

Adding is completely different to multiplication and division. We use adding to aid us in the multiplication and division, but computers use a different method.

[nhnifong]

A binary adder is a component of both integer and floating point multiplication in CPUs

Besides bit-shifting I'm not sure there are any other operations that can be performed without addition

[Xeldrak]

a+a=(1*a)+(1*a)=a(1+1)=2*a

thats all I can come up with

[Eric S]

If I remember right, the Principia Mathematica spent 900 pages working up to the proof that 1 + 1 = 2, and still got criticized for being incomplete. Admittedtly, the critics were using a different standard of complete.

[nhnifong]

If I remember right, the Principia Mathematica spent 900 pages working up to the proof that 1 + 1 = 2, and still got criticized for being incomplete. Admittedtly, the critics were using a different standard of complete.

haha, when you put it that way, it sounds like we have no chance of proving 1 + 1 = 2

[Nuke]

Adding is completely different to multiplication and division. We use adding to aid us in the multiplication and division, but computers use a different method.

http://en.wikipedia.org/wiki/Binary_multiplier

multiplications are done with adds and shifts so i would assume that would be disqualified. but the right binary bit shift, while is equivalent to a multiplication by two is neither multiplication nor addition.

Edited May 19, 2013 by Nuke

[jason0735]

come on guys 4-2=1+1, 2 to the power of 0

[Xeldrak]

Well, proving that 1+1=2 is not that hard. At least in modern maths....however you first have to come up with natural numbers (wich you can derive from axiomatic set-theory) and what "+" means - I have a book here somewhere that does all this in about 30 pages. Well, it defines not only natural, but up to real numbers.

Once, this is done - the prove of 1+1=2 is probably 2 lines long....

[K^2]

You can't really prove 1 + 1 = 2 in the framework of standard algebra, because in the frame work of standard algebra 1 + 1 is the definition of 2. More specifically, a sum of any two integers must be an integer. (You may replace integer with any other ring, including rationals, reals, etc.) So there exists an integer that is equal to 1 + 1. We assign label "2" to that integer.

You could build algebra differently, starting with a different set of definitions, but then you really have to specify what your axioms are before you can ask for anything to be proven.

Standard way to define natural numbers, however, is via addition of a unit.

2 ≡ 1 + 1

3 ≡ 2 + 1

4 ≡ 3 + 1...

So long as we agree that no element repeats (for example, I could have set 0 = 4 + 1, in which case we have numbers 0-4 with a Z₅ algebra) you get the set of natural numbers. Once you throw in the negative elements, you have your ring of integers. Therefore anything + 1 is just matter of definition. But then if you want to prove 2 + 2 = 4 in that framework, you actually have to construct a proof, albeit, a simple one.

P.S. Yes, there is a set-theory method for constructing a set of natural numbers, in which case 1 + 1 = 2 is a derived result. But that's not a terribly natural way of approaching counting, unless you happen to be a set theorist.

Edited May 19, 2013 by K^2

[3_bit]

If you're using binary math with a 2-bit adder with no overflow and just complement (invert each bit) the Accumulator, which holds the one in the binary form 01, it would result in 10, which is binary for 2.

[nhnifong]

How does set theory provide a way to create operators?

IOW what do you need to start with in order to invent the sequence [+ * ^ ...]

[Ziff]

I have an apple. You have an apple. I punch you in the face and take your apple. Now I have 2 apples, and I did it all without adding.

[Paprika]

haha, when you put it that way, it sounds like we have no chance of proving 1 + 1 = 2

Not with that attitude!

[Hyomoto]

I'll go ahead and take the dumbest approach.

The + sign indicates the method of its logic. This method is addition. Thus, 1+1=2 can only be solved with addition. The only way to change this is to take it completely into another context.

[ruiluth]

Addition is an elementary function. Proving that addition works is like proving that a plane is flat or a circle is round. Things like that just don't break down, and you can't prove something without breaking it down.

[Nuke]

I have an apple. You have an apple. I punch you in the face and take your apple. Now I have 2 apples, and I did it all without adding.

you win the thread

[rryy]

I GOT IT!

The character "1" looks a lot like the capital "I"! In 1+1, there looks like there are two "I"'s, or II, Roman numeral for 2!

Genius.

[Frederf]

It makes me wonder if the concept known as addition is unique to the performance of the job it does. In other words, is there any other operation which gets the same result as addition that isn't? If not then addition spans its own operation space and is complete leaving no room for an alternative.

[Person012345]

It makes me wonder if the concept known as addition is unique to the performance of the job it does. In other words, is there any other operation which gets the same result as addition that isn't? If not then addition spans its own operation space and is complete leaving no room for an alternative.

Well if it behaves in the same way as addition then it is addition, just by another name. I could define a new symbol called the flarg and then define it the same way as addition. And at that point, it IS addition.

[Kerbface]

I'm not sure why we need to "prove" that 1 + 1 = 2 when the concept of 2 is something we defined as a one and another one.