# Why does 1+1=2?

Discussion in 'General Philosophy' started by qfrontier, Mar 9, 2003.

1. ### rayzinnzRegistered Senior Member

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Exactly Exaphael. In a sense. But you're confusing math with language. 1+1=2, it doesn't matter wether you use this symbol or that symbol, it just so happens we've learnt the same symbols for math.

Imagine teaching a child the math behind 1+1=2, you would use symbols to help you, but only as a tool.

At every time in your life, if you have one of something and add another one of that something, you get two of those things. There is no example you can use to prove otherwise.

3. ### DaMenace123Registered Member

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That is not wrong. pretend it said A^2 - B^2 , which equals (A+B)(A-B), I'm just using A^2 - A^2 instead of A^2 - B^2. Seems every person I show this proof to feels they need to disprove it or something. The reason that it ends up being 1 = 2 is because you are dividing by (A-A), or zero. Whenever you divide by zero you get a messed up answer, that is why x/0 = undefined.

5. ### grimreaperRegistered Senior Member

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156
1+1=1

if you add a pile of sand to another pile of sand you will have one pile of sand.

with respect

7. ### rayzinnzRegistered Senior Member

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sand is a plural, suggesting its not "1"

8. ### Truth HurtsRegistered Senior Member

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1 + 1 does not equal 2

techincally 1 + 1 does not equal two
since the two objects can not ever occupy the exact same geographic location at the exact same time the two objects will never quite totally and evenly equal 2.

9. ### rayzinnzRegistered Senior Member

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But if two objects occupied the exact same geographic location at the exact same time wouldn't they equal 1?
Its because they don't that they equal 2.

10. ### Truth HurtsRegistered Senior Member

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the 2 objects that occupy the exact same geograhical location at the same time would not equal one either.
the object first described as one is a set definition of its properties. if purely and totaly mixed with the other object they are not one any more but one that is a more dense object.
if you could on an atomic level crush the 2 objects together they would collapse. as done in an atom smasher the smash to particles together and you see all the goodies inside. that doesnt sound like the answer of 1 or two to me.

11. ### coolsoldierRegistered Senior Member

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"pile" is singular.
1 pile (of sand) + 1 pile (of sand)= 1 pile (of sand).
The unit is the pile not the sand.

12. ### thefountainhedFully RealizedValued Senior Member

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2,076
Ok.

1 + 1 is not the same as
1 (unit of A, or X, or Hydrogen or etc) + 1 (unit of A, or X, or Hydrogen or etc).

1a + 1b is not the same as 1c + 1d

Once u add you a unit, u change the whole concept. Obviously
I gram + 1 gram is not the same as 1 liter + 1 liter
The first represents 2 grams and the second 2 liters.

In every system, there exist rules governing that system. The system at hand is a number system-- an abstract definition of natural phenonoma or a way to explain nature. In that system, its decimal deviant, the number one implies unity.
2 is DEFINED as 1 + 1.
Unless u change that definition, 1 + 1 is 2.

OF COURSE 1 + 1 can mean vbasdgsjkd if I define it as thus.

U cannot chose a definition within a system and redefine it at your whim.

1 + 1 is always 2 in the DECIMAL NUMBERING SYSTEM! End of argument.

The capital of the USA is Washinton DC. Not New York city because it has more commerce. The government-- the ruling body of the country(another conceptual definition) defines its capital(yet another conceptual definition) as Washington DC. And so it is the capital.

Why don't you REDIFINE H2O as e5rufyo part H and 48970 part O and then see where your argument takes you.

13. ### Truth HurtsRegistered Senior Member

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taking the con argument on the subject like 1+1 doesnt equal two lets nerds argue why it does.
(hey nerd your being being fucked with, and it is very funny)

14. ### CHRISCUNNINGHAMThe Ethereal ParadigmRegistered Senior Member

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280
The fact is that mathematics has no founded existence. It is conjured by our primitive brains as an attempt to understand existence itself. Math has no intrinsic meaning, it only has as much meaning as we imagine it to have.

15. ### buffysRegistered LoserRegistered Senior Member

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1,624
I'm new to forums in general and I just have to say how pleased I am with this thread. To me, all is right in the world when this much discussion can come from such a simple notion as why does 1+1=2? I really can't believe how many interesting thoughts have been tossed around here ... I think I'm home. I've heard a few people (in other groups) complaning about how this forum is just a bunch of 13 year olds swearing at each other but from my limited experience so far this is not at all the case. If this is representative of the rest of the threads I truely couldn't ask for more. Sorry for not adding anything to the 1+1 discussion, I just needed to say something about how great this place is.

16. ### buffysRegistered LoserRegistered Senior Member

Messages:
1,624
I'm new to forums in general and I just have to say how pleased I am with this thread. To me, all is right in the world when this much discussion can come from such a simple notion as why does 1+1=2? I really can't believe how many interesting thoughts have been tossed around here ... I think I'm home. I've heard a few people (in other groups) complaning about how this forum is just a bunch of 13 year olds swearing at each other but from my limited experience so far this is not at all the case. If this is representative of the rest of the threads I truely couldn't ask for more. Sorry for not adding anything to the 1+1 discussion, I just needed to say something about how great this place is.

17. ### lucifer_Registered Member

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1
Anyone who replied to this trying to explain why one plus sodding one equals two, is now stupider for having to feel the need to explain common sense.

I now hope you all burn in hell, have a nice day.

18. ### Blue_UKDrifting MindValued Senior Member

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1,447
A 5 page thread on why 1 + 1 = 2?

It's one of the axioms of arithmatic, and no one of yet has been able to break it down as far as I know.

I can prove, however, that 2 = 1. Start with a = b:

a = b

multiply both sides by a, then add (aa - 2ab) to both sides and then simply divide out the common factor!

aa=ab
aa + (aa - 2ab) = ab + (aa - 2ab)
2(aa - ab) = (aa - ab)
2 = 1

Simple, but flawed.

19. ### river-windValued Senior Member

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2,671
hm....ok, I see.

(a+b)(a-b)=aa+(ab-ba)-bb
ab=ba, so ab-ba=0, so the above =aa+ -bb or aa-bb. stupid foil

sorry for the mistake. yeah, math is messy. that's why I never liked it.

Blue_UK:
now there's a proof I can understand!!

20. ### rayzinnzRegistered Senior Member

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Well in that sense, 1pile+1pile can equal 1pile, or 2 piles, or 3 piles or 4 piles...

Or maybe set as a unit?

1 set of numbers +1 set = 1 set, 2 sets, or 3 sets...

I can't be bothered at the mo' explaining why this is wrong. Maybe you can figure it out.

21. ### CrisIn search of ImmortalityValued Senior Member

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9,199
I seem to recall having this debate some time ago and quoting this proof.

Why 1+1=2.

The proof starts from the Peano Postulates, which define the natural numbers N. N is the smallest set satisfying these postulates:

P1. 1 is in N.
P2. If x is in N, then its "successor" x' is in N.
P3. There is no x such that x' = 1.
P4. If x isn't 1, then there is a y in N such that y' = x.
P5. If S is a subset of N, 1 is in S, and the implication
(x in S => x' in S) holds, then S = N.

Then you have to define addition recursively:
Def: Let a and b be in N. If b = 1, then define a + b = a'
(using P1 and P2). If b isn't 1, then let c' = b, with c in N
(using P4), and define a + b = (a + c)'.

Then you have to define 2:
Def: 2 = 1'

2 is in N by P1, P2, and the definition of 2.

Theorem: 1 + 1 = 2

Proof: Use the first part of the definition of + with a = b = 1.
Then 1 + 1 = 1' = 2 Q.E.D.

Note: There is an alternate formulation of the Peano Postulates which replaces 1 with 0 in P1, P3, P4, and P5. Then you have to change the definition of addition to this:
Def: Let a and b be in N. If b = 0, then define a + b = a.
If b isn't 0, then let c' = b, with c in N, and define
a + b = (a + c)'.

You also have to define 1 = 0', and 2 = 1'. Then the proof of the
Theorem above is a little different:

Proof: Use the second part of the definition of + first:
1 + 1 = (1 + 0)'
Now use the first part of the definition of + on the sum in
parentheses: 1 + 1 = (1)' = 1' = 2 Q.E.D.

22. ### buffysRegistered LoserRegistered Senior Member

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1,624
man ... i really wish my understanding of equations was stronger but im beginning to get lost. I implore the more knowledgeable in this thread to try less ... numerical explanations.

I know that makes it harder for you but much of the last page in this stream is ALMOST incomprehensible to my (grade 12 math) mind.

I really find this an interesting discussion but i just dont have the background to follow the most (i assume) important parts.

I mean, Stephen hawking's book (a brief history of time) made sense to me for gods sake! you guys can do it too, i know it.

23. ### Blue_UKDrifting MindValued Senior Member

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1,447
Am I to understand that postulate = axiom and natural numbers = positive integers.

I was wrong in what I said earlier. "1 + 1 = 2" is not of of the basic axioms I was thinking of. They are suppost to be 'linearly independent'. That is, 'you can't deduce one from any of the others'.

Buffys, it's hard to write expressions in text only, so we use things like x^2 to mean x squared. I don't think there is anything too hard here, except perhaps the terms used.