Why 1+1=2?

Answer 1

No, 1+1 does not have to equal to 2. In fact, we have a sample of 1+1 not equal to 2 in reality too. One of my majors in university was mathematics and it talked about this question, why 1+1=2 in the class of Abstract Algebra. This involves group theory, which I won't have enough time nor space to type all that out here. In short, the addition, which we use the symbol, +, to signify, is a binary operation. Binary operation means that it takes two operands (in our case, it is 1 and 1). The result of this binary operation must also exist in the group, by definition. In this case, the result of 1+1 is 2 and 2 is in the integer group; therefore, this is a valid result. Some people may say that 1+1 = 10 (in base 2) is the idea of why 1+1 does not equal to 2. This is a false understanding. 10 in base 2 is equivalent to 2 in base 10; it is just that the representation is different. But the true 1+1 not equal to 2 example is time. Think about time in the military time system. Let's say it is 1:15 right now, what time will it 2 hours and 18 minutes later? The answer would be 3:33. But if I were to ask you what time is it 500 hours and 900 minutes later? The answer would be 21:27. If I were to tell you that the time would be 501:915, you will look at me like I have three heads because 501:915 does not make any sense in the milary time system. When you are something are equivalent, you are saying that when people tell you two different things, they both mean the same thing to you. But since 501:915 and 21:27 are not the same thing, this violates the basic logic of 1+1=2; therefore, 1+1 not necessarily equal to 2.

Answer 2

The reason 1+1=2 is that 1+a, for any a not 1, is not 2, given the Ring of integers with the recursive relationship of the binary operation of + under arithmetic of a decimal system. You can easily find the proof of 1+1=2 on the web, but the essense of the proof is that 1+a, or a+1 for any 'a' not 1 is something else, and hence leaving only one possibility for 1+1, which is 2.

Answer 3

Depends on the situation. In a particular finite field, GF(2), 1+1 = 0.
It just depends on how people started math. You make axioms and you go with it. You could define 1+1=3, but then you would have tell us how you would change number theory so that everything is right with the universe. It's just easier to do what everybody else does and stick with 1+1=2.

Answer 4

not necessary always 1+1=1 this depend on physical system in natural numbers 1+1=2 but in vectors some times 2 or o or sqare root of 2 and so on in other systems

Answer 5

because 2-1=1 :)

Answer 6

2 is just a symbol. If we have said 1+1=3 that might be true..it is our notio of interpreting 2 as it is.

Answer 7

well 1 dould equal 2
2 divided by 0 = A
1 divided by 0 =B
A = 0
B = 0
there fore, 1 = 2

Answer 8

that's the way addition works and our numbering system. you have a number in this case 1 and you add another to it in this case is 1 and the end result is you have 2. (If it were multiplication, you would only have 1).

Answer 9

Also

I+I=II
A+A=2A
2A-A=A
II-I=I
2-1=1

Answer 10

because the law of induction tells us that the next integer after one is one greater than that integer. And the well ordering principle says that it is the closest integer that is greater than one. So we name that integer two under the assumption that it is the next greater integer after one.