Please refrain from negative comments. It is not in the spirit of the forums, and this is most definitely NOT a stupid question.FulhamFan3 said:I'm going to answer this question with a question. What are Numbers? What is "one"? What is "two"? When someone answers that I got a simple one line proof to your stupid question.
Not a proof, but 2 is defined as the successor of 1 (under Peano), and hence satisfies the above requirement.afton said:Is there a proof that 1+1 = 2 ?
or we just accept it as it is ?
It's all a matter of definition. In most mathematical examples, 2 is defined to be 1+1, so the proof is rather trivial.But why is it so? I asked a mathematics professor who wrote
a book on Proof in Mathematics for university students pointed me
to read the Russell and Whitehead's Principia Mathematica.
Somewhere in the 500 pages of axioms and theorems
they're trying to prove by extending Peano postulates that
1+1 = 2.
Incorrect.But in 1931 Kurt Gödel with his Incompleteness Theorem
demonstrated that within any given branch of mathematics, there
would always be some propositions that couldn't be proven either true
or false using the rules and axioms.
It would be thesame thing.It would have to do with our perception of addition.For example if in school the kid were taught that 1+1=3 and 1+3=2 (that is to say the order 1,2,3 would be changed),then he would be convinced that one apple+one apple=3 apples.roger said:
I would think so. Each number represents a certain quantity of something. We defined the digits 0-9 to represent a fixed quantity. Hence if you put those quantities together the new quantity is your total. there's your proof.roger said:
2 drops are in the cupmatt grime said:The usual "counter argument" goes: I have a cup with a drop of water in it, I add another drop of water to it, then I look inside. How many drops of water are there in the cup
Still a circular argument :-) "being one more...." contains "one" in theloseyourname said:Did no one notice Dexter's post about this? If we called a collection of one object and another object three objects, then 1+1=3. The only reason it equals 2 as it stands is because that is what 2 is defined as. In an integer series, each integer is defined as being 1 more than the one it follows (roughly put).
This is the second time you've introduced Godel for no reason, and incorrectly. Godel's theorem actually requires that the system is strong enough to contain "the natural numbers" in any model of it.afton said:If we somehow can arrive at a definition of what is 'one' (in which Godel's Incompletness Theorem said we can't)
It isn't an argument at all - it's a definition. That's the whole point! This would be the argument:afton said:Still a circular argument :-) "being one more...." contains "one" in the
sentence. Imho the difficulties is from defining what is 'one'. If we somehow
can arrive at a definition of what is 'one' (in which Godel's Incompletness
Theorem said we can't) proving 1+1=2 would be much easier
I'm sorry,pal,this is after all,a science forum and any little/huge mistake must be corrected.loseyour name said:Water is defined as at least one molecule containing two moles of hydrogen and one mole of oxygen.
Therefore, any molecule or collection of molecules containing two moles of hydrogen and one mole of oxygen is water.
FulhamFan3 said:there is no difficulty in defining 1. 1 is defined as an isolated quantity. 2 is defined the whole number quantity after that.
nope. Numbers can never have an entirely abstract basis. How would you teach someone to count just using numbers? You'd have to show somewhere the one is singular and two is twice that. They have to represent some sort of quantity whether its a unit of length, area, volume or apples. It's only abstract in the sense that it's a general unit basis.roger said:But why should quantity even enter into the argument ? ( when trying to define 1)
After all quantity is physical, so shouldn't we be able to define 1 purely abstractly, without resorting to physical principles such as a quantity ?