Is "1+1" provable?

[millwood]

I remember seeing what was suppose to be a proof of "1+1=2" somewhere,

proving 1+1=2 is easy. it is much toughter to prove 1+0=0. Here is my proof:

0=0+0+0+0+....

0=(1-1)+(1-1)+(1-1)+(..)....

0=1+(-1+1)+(-1+1)+(-1+1)+...
0=1+0+0+0+0+0+...
0=1+(0+0+0+0+...)
0=1+0

done.

🙂

 

[millwood]

Re: Re: Re: Re: Is "1+1" provable?

Most of the participants are not concerned with real-world applications, but try to discuss it theoretically without regard to practical usefullness.

I just couldn't resist it😉

yeah. That also reminds me of those discussions on inverting superiority, why resistors and heatsink resonance impact sound, etc.

people gave completely zero regards to real world experience and talk about theories in vaccum. As long as I heard it and my buddy heard it, it is OK.

 

[Christer]

proving 1+1=2 is easy. it is much toughter to prove 1+0=0. Here is my proof:

0=0+0+0+0+....

0=(1-1)+(1-1)+(1-1)+(..)....

0=1+(-1+1)+(-1+1)+(-1+1)+...
0=1+0+0+0+0+0+...
0=1+(0+0+0+0+...)
0=1+0

done.

🙂

A good lesson in why one has to be careful with infinities.

 

[Elso Kwak]

1+1=?

Hi,
This discussion is way over my head but for me:
1+1= 3
Now do I have to prove it?

 

[sam9]

"0=0+0+0+0+....

0=(1-1)+(1-1)+(1-1)+(..)....

0=1+(-1+1)+(-1+1)+(-1+1)+...
0=1+0+0+0+0+0+...
0=1+(0+0+0+0+...)
0=1+0 "

Did you once make a living playing Three Card Monty with the yokels?

 

[elizard]

proving 1+1=2 is easy. it is much toughter to prove 1+0=0. Here is my proof:

0=0+0+0+0+....

0=(1-1)+(1-1)+(1-1)+(..)....

0=1+(-1+1)+(-1+1)+(-1+1)+...
0=1+0+0+0+0+0+...
0=1+(0+0+0+0+...)
0=1+0

done.

🙂

Well, after posting that 1+1=2 is an axiom that we take to be true, i thought about it some more and it didn't sit with me. So what i did is i googled for definition of addition (which seemed to be the key in proving this) and lo and behold, i found it!
So, using that definition i very simply proved 1+1=2.

So what does this have to do with your post millwood? Well, one of Peano's axioms states that 1+0=1. Its one of the rules of addition, and you don't prove rules. Rules you take to be true within the domain they encompass (addition in this case). Rules are what actually define your domain, so its 1+0=1 (along with the other axiom stating that a+b*=(a+b)*) that tell us how to use addition with natural numbers.

edit: One more thing. Because 1+0=1 is an axiom, or a 'rule' defining addition, when using peano's view of addition, you can never prove 1+0=1. This is because in your proof you will be required to use the axioms defining addition (trust me, you would need both), but since you're trying to prove 1+0=1, you can't use it in your proof. The proof would be unsound logically because your proof would turn out to be the following: "IF 1+0=1 is true, then 1+0=1 is true" (Classical example of a misused proof like this is St. Anselm's ontological proof of God.)

 

[Christer]

Re: 1+1=?

Hi,
This discussion is way over my head but for me:
1+1= 3
Now do I have to prove it?

No, that's trivial. You've got two "1"s and one "+", that makes
three in total. 🙂 🙂

 

[elizard]

Re: 1+1=?

Hi,
This discussion is way over my head but for me:
1+1= 3
Now do I have to prove it?

Well, if you want to be using traditional arithmetic/addition, then you will be wrong. If you want to make up your own addition system, then you are free to say that 1+1=3, and then deduce what 1+2, 1+5, 5+7, etc will be from there on. Nobody's restricting you to using normal addition (well, maybe the fact that everyone else is using it, but if everyone else jumped off a bridge ....)

 

[Richard C]

A more relevant question would be "what is the point of this discussion on this forum?"

I'm going to start a thread called "going anywhere nice for your holidays?"

And why not🙂

 

[elizard]

A more relevant question would be "what is the point of this discussion on this forum?"

Well, it is posted in 'Everything Else', so I'm assuming its fitting for everything else. The point of this thread, as you may have noticed, is to try to prove (or disprove if possible) that 1+1=2

 

[Richard C]

In that case I look forward to the conclusion.

 

[elizard]

I believe I've stated the conclusion long ago, then Christer re-stated it. 1+1=2 IS proveable (as demonstrated).

 

[Tobbe_L]

millwood: As far as I remember it was far from easy. "Principia Mathematica" uses logic on a level which I do not understand (I have a degree in engineering physics which means that I know enough math to recognize a complicated proof 😉 )

For those of you that did not know: "Principia Mathematica" was basically an attempt to prove that math is self-consistent (this was before Gödel, I thing the book was written around 1900), it is an impressive work even though they of course did not succed.

 

[Christer]

Well, it is posted in 'Everything Else', so I'm assuming its fitting for everything else. The point of this thread, as you may have noticed, is to try to prove (or disprove if possible) that 1+1=2

Well, I started the thread but I really don't know what the
point is, except that starting a new thread was my only way
of asking millwood what he meant in the thread that was
closed. I never expected a lot of new similar discussions
emerging. Stupid me, how could it have been otherwise? 🙂

Edit: I should add, that millwoods original claim I wanted
clarified was not about proving whether "1+1 = 2".

 

[millwood]

Re: 1+1=?

1+1= 3
Now do I have to prove it?

that's so easy.

1(wife)+1(husband)=1(wife)+1(husband)+1(kid)=3.

find one that's more challenging, 😉

 

[ThorstenL]

Konnichiwa,

I don't want to start another thread here, but millwood also said;

Originally posted by millwood

Again, awareness is an acquired taste and not everyone is gifted with it.

As far as I understand, awarness is a consciousness and knowledge, and this, unlike taste, is not biased. It is also not a gift, but something one gains if he follows the right path.

Well, awareness is an interesting subject.

You and millwood remind of the two man who blundered into an elephant in darkness from opposite direction and groping over it's bulk feel some small areas and consider they now know all there is to know about elephants. How about taking a few steps back, switching the light on and maybe studying the mating habits of Elephants, which I think are much more interesting....?

Sayonara

 

[ThorstenL]

Waking up and awareness....

ON WAKING UP
by Anthony de Mello, SJ

Awareness means waking up. Most people, even though they don't know it, are asleep. They're born asleep, they live asleep, they marry in their sleep, they breed children in their sleep, they die in their sleep without ever waking up. They never understand the loveliness and the beauty of this thing that we call human existence.

You know, all mystics -Catholic, Christian, non-Christian, no matter what their theology, no matter what their religion -- are unanimous on one thing: that all is well, all is well. Though everything is a mess, all is well. Strange paradox, to be sure. But, tragically, most people never get to see that all is well because they are asleep. They are having a nightmare.

Last year on Spanish television I heard a story about this gentleman who knocks on his son's door. "Jaime," he says, "wake up!" Jaime answers, "I don't want to get up, Papa." his father shouts, "Get up, you have to go to school." Jaime says, "I don't want to go to school." "Why not?" asks the father. "Three reasons," says Jaime. "First, because it's so dull; second, the kids tease me; and third, I hate school." And the father says, "Well, I am going to give you three reasons why you must go to school. First, because it is your duty; second, because you are forty-five years old, and third, because you are the headmaster."

Wake up, wake up! You've grown up. You're too big to be asleep. Wake up! Stop playing with your toys.

Most people tell you they want to get out of kindergarten, but don't believe them. Don't believe them! All they want you to do is to mend their broken toys. "Give me back my wife. Give me back my job. Give me back my money. Give me back my reputation, my success." This is what they want; they want their toys replaced. That's all. Even the best psychologist will tell you that, that people don't really want to be cured. What they want is relief; a cure is painful.

Waking up is unpleasant, you know. You are nice and comfortable in bed. It's irritating to be woken up. That's the reason the wise guru will not attempt to wake people up. I hope I'm going to be wise here and make no attempt whatsoever to wake you up if you are asleep. It is really none of my business, even though I say to you at times, "Wake up!" My business is to do my thing, to dance my dance. If you profit from it, fine; if you don't, too bad! As the Arabs say, "The nature of rain is the same, but it makes thorns grow in the marshes and flowers in the gardens."

 

[Elso Kwak]

Re: Wake up Call

ON WAKING UP
by Anthony de Mello, SJ

Awareness means waking up. Most people, even though they don't know it, are asleep. They're born asleep, they live asleep, they marry in their sleep, they breed children in their sleep, they die in their sleep without ever waking up. They never understand the loveliness and the beauty of this thing that we call human existence.

You know, all mystics -Catholic, Christian, non-Christian, no matter what their theology, no matter what their religion -- are unanimous on one thing: that all is well, all is well. Though everything is a mess, all is well. Strange paradox, to be sure. But, tragically, most people never get to see that all is well because they are asleep. They are having a nightmare.

Waking up is unpleasant, you know. You are nice and comfortable in bed. It's irritating to be woken up. That's the reason the wise guru will not attempt to wake people up. I hope I'm going to be wise here and make no attempt whatsoever to wake you up if you are asleep. It is really none of my business, even though I say to you at times, "Wake up!" My business is to do my thing, to dance my dance. If you profit from it, fine; if you don't, too bad! As the Arabs say, "The nature of rain is the same, but it makes thorns grow in the marshes and flowers in the gardens."

Goeiedag,
I am going to print and frame the above quote and post it above my bed!😎
I never realised I procreated my daughter while sleeping!
Well it must be that I did not realise it because I was sleeping.....
This post of yours is even better than the one I found lately: (rule # 5 of audio)🙄
"If it is well designed, it can't sound good; because someone actually applied thought to the product."😎
Tot ziens.
Elso/Awake and well

 

[planet10]

Re: Waking up and awareness....

]ON WAKING UP

Good essay...but unfortuneatly only those awkw or in the process of awake will having any idea what the guy is talking about....

dave

 

[ThorstenL]

Re: Re: Waking up and awareness....

Konnichiwa,

Good essay...but unfortuneatly only those awkw or in the process of awake will having any idea what the guy is talking about....

Well, as he says.....

"I hope I'm going to be wise here and make no attempt whatsoever to wake you up if you are asleep. It is really none of my business, even though I say to you at times, "Wake up!" My business is to do my thing, to dance my dance. If you profit from it, fine; if you don't, too bad!"

Sayonara