can 2+2 = anything other than 4?

Question

i have a bet running with a friend about logic. he thinks that no fact can be disproved with consistant logic. i think it can. leaving the bet aside for a moment can anyone prove logicaly that 2+2 dose not = 4?

Answer 1

The modular (and clock) arithmetic answers are correct, but I think they miss the point a bit, since in any modular arithmetic you still have 2+2 = 4 mod n. Let's suppose we are using the natural numbers with the usual addition.

The recurring decimal answers are just stupid, 1 = 0.9999... recurring (as shown in fact by the first answer here), so all of these answers are either irrelevant or wrong.

The '2' is just a symbol arguments possibly have some merit, but you should be careful. In Indianna in 1872 (or thereabouts) it was ruled by State legislature, that the value of pi is 4. Obviously this creates problems, if you go to Indianna you won't find many buildings that were designed in 1872. (Their mistake of course was that they didn't alter the representation of all the other numbers they where using accordingly).

I'm not really a logician so I don't know the answer to this off the top of my head, I'm pretty sure that we don't have a satisfying answer here (sorry if we have but I missed it).

Perhaps a good place to start looking for a serious discussion on this kind of topic would be to understand what a Peano system is (wiki it, I'm not explaining that here, 'tis an axiomatic description of the natural numbers). I've also heard that Bertrand Russell gave a proof that 1+1 =2 in Principa Mathematica, although I haven't read that and I don't know precisely where you can find it.

Answer 2

If you do it in base 3, then 2+2=11.
If you do it in base 4, then 2+2=10.

Answer 3

Following on in a similar vein to David F's answer, you can always add extra conditions to change the result.

Doing it in different bases is one way; performing addition modulo 2 or 3 is another (where 2 + 2 would be 0 or 1, respectively).

Only by *completely* stipulating the problem can you eliminate this ability to warp the question - the 'addition' operation needs to be exhaustively defined for any proof to be conclusive, and even then it would only hold for those conditions.

Hope that helps!

Answer 4

22

Answer 5

If you were on a clock with only the numbers 1, 2 and 3, 2+2 would equal 1.

Answer 6

Numbers in themselves are an abstraction - think of them as models. 1+1=2 is a conceptual and quantitative result (base 10 addition) that singular entities combined produce double of each e.g. 1 car + 1 car = 2 cars. But, 1 droplet + 1 droplet = .....1 droplet ! In other words, the POINT OF REFERENCE (and thus the "laws" or facts that hold in THAT reference) is what tips the scale.

Base 4 addition would give 2+2=10. I believe most so-called "facts" are relative (like everything else).

Answer 7

Yes. 2+2 can equal to any thing you want it to be. Really, what is (2)? (2) is just a symbol. What if I wanted this symbol (2) to equal four. Its hard to comprehend that, but that is possible. So, actually 2+2 would of been 8. So every time I changed the value of this symbol (2) it gives me a different answer.

Answer 8

The sign "2" is a representative of the amount "two". It could be used to represent any other numeral and therefore, 2+2 could equal anything at all. But what do I know, I'm just a high school algebra student.

Answer 9

In a mathematical sense it is right but the purpose of th number 2 universally known as meaning 1+1...is transient..therefore in this real world 2+2 is equal to 4...but in a quantum sense it might be something completely different....it is based on perception....similar to the way we perceive colours......differiing wavelengths lead to our brain perceiving that as a blue or red...etc etc...

Answer 10

i say that 2*2 = 4 is wrong.
say
- 20 = -20
16-36 = 25-45
16-36 + 81/4 = 25-45+81/4
4^2-2*4*9/2+ (9/2)^2= 5^2 - 2*5*9/2 + (9/2)^2
(4-9/2)^2= (5-9/2)^2
square root of it
(4-9/2) = (5-9/2)
4 = 5
if you say 2+2 = 4 then
2+2 = 5
so u'r wrong