# Why does 1+1=2?

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

1. ### bold standardRegistered Senior Member

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77
Re: Anti-Matter

Oh, right yeah. I was being overly simplistic, I don't think matter + antimatter is exactly the same as 1+(-1), because antimatter is actually something that exists with a value, not just the absence of something that exists with a value so it's more complicated than just a -1. I was just trying to show that two entities with conflicting natures can combine to cancel each other out, that's not a defiance of mathematics. It's totally in conformity with the law of causality, logic, mathematics etc. Math is just a language for logic.
A lot of people seem really hung up on the language issue. You have to be consistent with your ideas here. If you are talking about a matter particle and an anti-matter particle, you are talking about two particles. That's what it means to add them. Physically combining the two to see what reactions occur isn't adding them. It's combining them.

3. ### MacMRegistered Senior Member

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10,104
We agree

boldstandard,

I agree. It was just that you did it in the context of = 0. The combination only creates a new form not "0". But you seem to have understood that.

5. ### turbostasisRegistered Member

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someone tried to proove 1+1=0, and the proof was wrong. it was a disertation at UIC. it was neat if you can understand the notation.

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10,104
+/-

turbo....,

8. ### turbostasisRegistered Member

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11
no the proof was 1+1=0, it was very long, very wrong and very interesting

9. ### thefountainhedFully RealizedValued Senior Member

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2,076
WOW, This argument again????????

This is a ridiculously stupid debate.

1+1 = 2 because we are using a number system, this time decimal and the rules of that format dictate that
1+1 =2!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

Simple as that!

Last edited: Apr 21, 2003
10. ### firebrandRegistered Member

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12
Accountant, 1 + 1 = 3

Lawyer, 1 + 1 = 33% and who cares about the rest

Doctor, 1 + 1 = unobfuscated inorganic linguistic simplicity!

Philosopher, 1 + 1 = well. let's consider...

Physicist, 1 + 1 = non-symmetrical dynamic matrix system.

CEO, 1 + 1 = layoffs!

4 year old child, 1 + 1 = 2 DUMMY!

11. ### DarkEyedBeautyPirate.Registered Senior Member

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730
Math is a game. That through classes we slowly learn the rules to. It's just handy that we can symbolize the number two by an apple and another apple, that the number can have an image, can have a meaning.

12. You're wrong.

(A^2)+(-A^2)
That is what you wrote.
Let's say A=1

(1^2)+(-1^2)=?
(1)+(1)=2
Therefore, (A^2)+(-A^2)=2, if A=1

This is what you also wrote:
(A*A)-(A*A)
A also equals 1.

(1*1)-(1*1)
1+(-1(1))
1+(-1)
1-1
1-1=0

Therefore, (A*A)-(A*A)=0, if A=1

0=2 is not true.
Considering this,
the original statement itself was invalid.

A^2-A^2 does not equal (A*A)-(A*A)

13. ### rayzinnzRegistered Senior Member

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Why does 1+1=2? Hey man you were born into this reality and there's nothing you can do about it does you may aswell just accept that 1+1 will = 2 as long as your in your physical body. I mean, why does 10/3*3 = 9.9 recuring and not 10? Thats more strange if you ask me.

14. ### Quigly......................... .....Registered Senior Member

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1 + 1 may not always equal two

It all depends on how you look at it and what attribute you put to it. You could always say 1 (pair of Units) + 1 (pair of units) = 4 units
thus-- 1+1=4

but cut and dry= 1 + 1 = 2

1 Human + 1 Human = 2 Humans
Inside the human results in Millions and millions of other units... So there is still 1 + 1 = 2 but if you think that the attributes of that 1 item consist of millions of parts then the number could be 1 + 1 =any number or infinite if applying all attributes and properties consistent with that unit. any thoughts?

15. ### river-windValued Senior Member

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2,671
redoubtable, here is a simpler method to disprove this.

1)A*A - A*A = A^2 - A^2 let's assume this is true for now
2)A^2 - A^2 = A(A-A) ok, that works. left side to exponential notation, the right side went to wultiplication notation, and then polled out a common multiplier.
3)A^2 - A^2 = (A-A)(A+A) BEEEP BEEEP ERROR
ignoring the left side of the equation, he went from A(A-A) in number 2 to (A-A)(A+A) in number 3. A(A-A)!=(A-A)(A+A), according to the rest of his own proof. wrong assumption leads to a wrong conclusion.

proof:
Assume A(A-A)=(A-A)(A+A)
divide both sides by (A-A)
A=A+A
By definition of the set of intergers, a number A cannot equal A added to itself, given that the set maps one-to-one on the addition function. so A+A=A+A, and A=A, but A!=A+A. Therefore, given that everything else is accurate, there is a fault in the transition from A(A-A) to (A-A)(A+A).

if you fix that bit, you get
A*A - A*A = A^2 - A^2
A^2 - A^2 = A(A-A)
therefore
A(A-A) = A(A-A)
Dividing both sides by (A-A) gives us
A = A
1 = 1

and it works! wow.

however, your (redoubtable) method has a problem, too:
you have
1)(A^2)+(-A^2)
2)That is what you wrote.
3)Let's say A=1

4)(1^2)+(-1^2)=?
5)(1)+(1)=2
6)Therefore, (A^2)+(-A^2)=2, if A=1

The problem here is that if you set A=1 then you don't get to line 4 from the orignial assumption.
1)(A^2)-(A^2)
2)clarifly subtraction
3)(A^2)+(-1)(A^2)
4)assume A=1
5)(1^2)+(-1)(1^2)
6)simplify exponants
6)(1)+(-1)(1)
7)1+(-1*1)
8)1-1=0
this side of the equation =0, not 2

a more direct method:
5)(1^2)+(-1)(1^2)
6)multiply out (-1)=-(1) because of the rule of transity, IIRC basically, -(1)=-1(1)=-1
7)(1^2)+-(1)(1^2)
8)(1^2)+-(1)(1*1)
9)(1^2)+-(1*1*1) again, multiplying out
10)(1*1)+(-1) because (-1)=-(1) and (1*1)=(1^2), by definition
11)(1)+(-1)
12)1-1=0
again, this side of the equation =0, not 2

DaMenace123's statement is still wrong, though, according to the invented rules of addition, and ontop of that the invented rules of equality, multiplication, and exponentiation.

edit: oh, wait
if you do the multiplication 1st
(A^2)-(A^2)
(A*A)+(-A*-A)
and A=1, the you get
(1*1)+(-1*-1)
(1)+(1)=2

This is why the Defninition of exponentiation states that you have to take care of the exponants first. As I've said before, if something small in the situation changes, and Math falls apart. It's all based on a rigid set of rules, and it only works in certain cases, and in a certain order.

Last edited: May 15, 2003
16. ### Quigly......................... .....Registered Senior Member

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901
"1 + 1 may not always equal two
It all depends on how you look at it and what attribute you put to it. You could always say 1 (pair of Units) + 1 (pair of units) = 4 units
thus-- 1+1=4

but cut and dry= 1 + 1 = 2

1 Human + 1 Human = 2 Humans
Inside the human results in Millions and millions of other units... So there is still 1 + 1 = 2 but if you think that the attributes of that 1 item consist of millions of parts then the number could be 1 + 1 =any number or infinite if applying all attributes and properties consistent with that unit. any thoughts?"

To Add on to this: Lets take this example:

2 parts hydrogen 1 part oxygen =1 part H20 or Water
2+1=1

Any thoughts on Mixtures?...

17. ### MacMRegistered Senior Member

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10,104
Good

Quigley,

I like that one.

18. ### rayzinnzRegistered Senior Member

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Nice one Quigley.

So 1 + 1 of one thing can = 1 of another thing, or 1 + 1 can = lots of another thing. 1 letter "a" + 1 letter "t" = one word "at" to think up a random example. Personally I think this is a law of the universe.

In fact my biology book teaches that in the levels of a living system the sum of the total = more than the sum of its components. e.g. join atoms together makes 1 molecule, join some molecules together and you get a cell (and life).. and so on.
Join lots of neurons together and intelligence (ha) appears out of nowhere.

But in pure math 1+1=2 and always will.

BIOLOGY Campbell & Reece 2002

19. ### BillClintonsCigarRegistered Senior Member

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160
Yeah that works, on a level, but it doesn't work, on another. Surely the equation is two half parts of hydrogen, and one part oxygen! Two half parts = one part, plus one part, equals two parts.

(Welcome)

20. ### Quigly......................... .....Registered Senior Member

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901
ok BillClinton...

It is one part ...yet that one part would not equal one half it would represent itself as 1 unit.

you put two units together ...1 Unit Hydrogen + 1 Unit Hydrogen + 1 Unit Oxygen = 1 Unit Water..

Stop trying to prove me wrong or next time you walk by a tree I will have one of my Ninja monkey's kill you with a throwing banana... They suck, take my word for it.

21. ### turbostasisRegistered Member

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and how many units is methaine? the composition of elements is not math in it's pure form.

22. ### river-windValued Senior Member

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2,671
right. you've hit the nail on the head. So then where did math in it's pure form (abstracted from real-world objects) come from?

given that there are instances in non-classical math where 1+1!=2, I see Math outside of the real world is more flexable, in it every single thing is possible. It all depends on where you start (ie, what is the definition of the '+' sign, what number set are you working with, etc)

1+1=2 in common discussion, AFAICT, because simple integer math was the form of math which most closely reslembed the world. It was more often used by non-mathimatitions, and therefore remained in most people's minds as the entire definition of the word "Math". However, this math does not represent all of what occurs in Nature, nor does it represent all the math available in the infinate number/operation space.

23. ### ExaphaelRegistered Member

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1
This is so simple

1+1=2 for one reason only: because you say it does.

Its probably safe to assume your symbols are from the mathematical system that most people use.
For the sake of this argument it is assumed that the original question implies the use of common mathematical meanings.

Within this FORMAL SYSTEM, the rules of the system dictate how the symbols may be used to create true statements and how they may be used to create false statements.

The standard defnition of those symbols, displayed in the order they are given represent a true statement. That's all.

You might make up your own mathematical system wherein the character '1' could have two meanings; it could represent either three units or five units. In the same respect the character '2' could also have two meanings; four units or ten units. If then the symbols '+' and '=' have the same meaning as in common math then the statement 1+1=2 could be both true and false.

The difference between the abstract formal system that I described where symbols could have dual meanings is that common mathematics is useful and meaningful. Its rules parallel the rules of that real-world objects follow. If I own a car that gets twenty miles per gallon then I know I need to buy five gallons of gas to travel one hundred miles.