In all of my mathematical life I have never seen anyone prove 1+1 to be 0, 3 or anything strange like that. If someone could provide me with a link that shows me this I would love it. I’ve always had people tell me this, but no one has ever proven it. The only way you can make 1+1 not equal 2 is using some BS language trick (there are no mathematical tricks). 1+1 is always 2!
The only thing I can think of that comes close to this is when a physic’s professor was talking about what one is. “What’s one person? We’re constantly breathing in and out new molecules, dead skin is falling off, etc…” Non-mathematical people always say that 1+1 doesn’t always equal 2, please, enlighten me.
[quote]In Principia (Whitehead & Russell) “1” is defined as the class of all unit
classes; probably a good book to avoid for most readers. Other possibili-
ties include Frege’s “Foundations of Arithmetic” or references to Peano’s
Postulates. Grappling with the axiomatic logic is not suitable for most of
us and these readings are difficult. Let me attempt an inadequate simplifi-
cation. Frege would say that a number “belongs to a concept” and is an
extension of that concept and then statements about numbers correspond to
“identities of concept”.
In the sense of counting, one apple and one orange represent identical
concepts even if apples are not oranges, so we write 1 = 1. Now 1 + 1 or
for that matter 1 + 1 + 1 + 1 + 1 + 1 (repeating) are represented in the
sense of identity by other symbols which, if arabic numerals are used, we
write as 2 or 5. The symbols are just compact notation for representation
of an identical “concept”. Frege stated that number is not anything
physical nor is it subjective. This may not be very satisfying but deep
philosophical questions about numbers may always remain unanswered in very
satisfying ways.[/quote] mac-2001.com/maths/russell.htm
Another link.
But have you seen anyone prove that one plus one DOES equal two?[/quote]
My math professor…
It takes about 1 page to prove that one plus one equals two. As I remember, you use a proof by contradiction. Suppose that one plus one does not equal two. Then by the laws of addition, there exists some other number that one plus one equals… the proof goes on from there, and gives clear evidence that there can be no other solution.
“by the laws of addition, there exists some other number that one plus one equals”
If you’re going to start throwing laws around, you could just as easily say that by definition 1+1=2. But I’m pretty sure the Supreme Court threw that one out earlier this week.
It all depends on what type of ones you’re adding together. My one salary plus my wife’s one salary sure don’t equal two salaries after taxes.
Yeah. I am only trying to distinguish between “fact” and “opinion”.
This distinction is important when we debate. I think “[color=blue]blue[/color]” is the best color. That’s just my opinion. But, that this is my “opinion” is a “fact”.
[quote=“jeff”]“by the laws of addition, there exists some other number that one plus one equals”
If you’re going to start throwing laws around, you could just as easily say that by definition 1+1=2. But I’m pretty sure the Supreme Court threw that one out earlier this week.
[/quote]
This is basic algebra… We use symbols to represent concepts like one, two, addition, and equality.
But I’m guessing your argument is a joke anyway… Because the Supreme Court did not “throw that one earlier this week” as stipulated.
Maybe you make a lot of simple factual mistakes such as this one. If that’s the case, perhaps the taxes you complain about could be minimized by hiring a competent accountant.
But have you seen anyone prove that one plus one DOES equal two?[/quote]
I did, just this morning. It’s hidden in one of the links I posted. Those two guys wrote a 326 (I think) page book proving 1+1=2. I’d go back and look, but I’m on a slow crappy connection right now ( :x ) and don’t want to spare the clicks.
[quote=“twocs”][quote=“jeff”]“by the laws of addition, there exists some other number that one plus one equals”
If you’re going to start throwing laws around, you could just as easily say that by definition 1+1=2. But I’m pretty sure the Supreme Court threw that one out earlier this week.
[/quote]
This is basic algebra… We use symbols to represent concepts like one, two, addition, and equality.
But I’m guessing your argument is a joke anyway… Because the Supreme Court did not “throw that one earlier this week” as stipulated.
Maybe you make a lot of simple factual mistakes such as this one. If that’s the case, perhaps the taxes you complain about could be minimized by hiring a competent accountant.[/quote]
This is an interesting twist. If it is algebra rather than arithmetic then the
plot thickens.
1+1 = 2 assumes that there is no synergistic or redundant relationship between the first 1 & the 2nd 1.
I’m not a mathematician so have to think of this in pictures.
A man is operating a conveyor belt along which an object is moving. 1 is the symbol representing this picture. We add another 1 ie another man
doing the same thing. Now if they both are in free space with no interaction between them then the sum will be 2 . But if they interact in the same space then the answer could be very different eg if the 2nd man is actually positioned on the conveyor belt of the first then his package will be moving at twice the speed (the speed of both his conveyor belt & the one he is standing on ) . Synergy (ie a result where the sum is greater than the addition of the 2 component parts will occur) creating a result greater than 2. Alternatively if the 2 nd mans conveyor belt sends his package in the opposite direction to the first then there will be redundancy (ie a result where the sum is less the 2 compenent parts) leading to a result less than 2. Redundancy put more simply: Add 2 men
running at 10 miles an hour does not produce a speed of 20 miles an hour. ie 10 + 10 = 10 simplifies to 1+ 1 = 1.
To the point that there is a 326 page book proving that 1+1 = 2 .
There are several books a varying lengths that claim to prove that
aliens are regularly abducting & experimenting on us. And for that matter very few books (I think there is only 1) that set out to prove that aliens are not abducting us. The high volume of work in favour does not necessarily mean that it is true.
Yeah. I am only trying to distinguish between “fact” and “opinion”.
This distinction is important when we debate. I think “[color=blue]blue[/color]” is the best color. That’s just my opinion. But, that this is my “opinion” is a “fact”.[/quote]
Yes I get it. Problem is , only you know it is a fact. Earlier you described a fact as something that can be proved true or false. How do you prove that your opinion is that that blue is your favorite colour?
This reminds me of that interesting statment:
“I always tell lies” If you did always tell lies then you cannot use this statement to communicate the fact since this would be a true statement & thus invalidate your claim to always tell lies …
Then this is your problem and we’re speaking to totally different languages. In the language of mathematics things can be proved. 1+1=2 or 1+1 doesn’t not equal 2. There is no in-between (ie. 1+1=2 if… but 1+1 does not equal 2 if…) I don’t know how I can make it any clearer then that.
The examples you’re giving are utter nonsense. If you try proving that 1+1=2 (or does not equal 2), let’s see how many pages it takes you.
Then this is your problem and we’re speaking to totally different languages. In the language of mathematics things can be proved. 1+1=2 or 1+1 doesn’t not equal 2. There is no in-between (ie. 1+1=2 if… but 1+1 does not equal 2 if…) I don’t know how I can make it any clearer then that.
The examples you’re giving are utter nonsense. If you try proving that 1+1=2 (or does not equal 2), let’s see how many pages it takes you.[/quote]
Wether its nonsense or not is presumably a matter of opinion.
Since you are so certain that 1+1 = 2 & cannot equal any other number & from your selection of my quote are implying that you are a mathametician then I think the burden of proof is on you.
All you have done is said that there is a 326 page book that does prove it . That is not proof as I have illustrated with my Alien example.
Some one else already has, that’s why it’s called a proof. I can read the book and try to explain it to you if you like, but what good would that be. If you already believe it to be true or not, I can’t change your mind. What I’m trying to get at is with math there are no suprises, tricks or magic. You may be right in thinking that I don’t understand the proof that makes ones plus one equal two, but I do know that there hasn’t been a proof made that says otherwise.
When I saw the proof for 1+1=2 (from that book) I didn’t even understand it (there’s a picture of it on the web somewhere), there were a bunch of symbols used I have never seen (that’s probably what the rest of the book explains).
Let me try to help you with your visual examples. Maybe you should use angles, series of things (1, 11, 111, 1111, 11111) or simple shapes. I understand what your getting at with your proof of 1+1=2 and I’ll be sure to read up on it this weekend and bring you back a full report.
I was talking with and older and wiser (and grumpier ) friend of mine earlier today about this 1+1 thing. We had a nice talk, then he sent me this email later on. I hope someone enjoy’s it as much as I do.
(he asked to be reffered to as Dr. Enura ezz)
[quote=“Dr. Enura ezz”]Does 1+1=2?
This depends on if you are capable of talking from your ass. You see if you
can speak from deep down where the shit lines up to parachute into the
toilet, you can create your own reality where those so called laws of
science and nature no longer apply and perhaps never existed.
You might ask,“isn’t reality just what is real?” The answer is NO. Those
who can speak from the sphincter live in a world entirely or partially
(depending on their reality) of their own creation. Therefore, 1+1 does not
have to equal 2. 1+1 can equal a Toyota Corolla. Rain may no longer be
called rain. It can be called sazbach, and it’s no longer wet. It’s jizzy.
Of course, it no longer contains the properties of rain or water for this
is my reality. It all depends on what reality you subscribe to (or in
technical terms how loud the voice in your ass is). Most people subscribe
to basic cable. I on the other hand use pay per view. So, in my reality 1+1
does not equal 2. It equals Jennifer Lopez, Sandra Bullock, and myself in a
wild bi-sexual sexfest. You dig?
You might ask,“Does talking from your ass hurt?”
For some it might but for the most part it only irritates those around
them. Those around you might think you are pretentious, dillusional, or
just plain crazy. However, that is their reality and their rules don’t
apply to you- neither does gravity for that matter.[/quote]
I don’t want to convice anyone that 1+1=2 (or anything for that matter), I think I just had a natural reflex to keep people from getting dumber. Maybe this is what’s missing from the conversation. There are fatcs and beliefs, when people start spreading their beliefs as facts things get clouded.
How can you separate a fact from a belief? Maybe that’s up to the individual. Forget trying to proof 1+1=2, how do you proof God exists (or doesn’t)? (just an example, I’m not trying to start up something else). I’ll stop there.
Perhaps I could have chosen a better quote. Wittgenstein has had a huge and controversial impact on contemporary linguistic thought. In short, he posited a division between that which is real and that which language depicts. For example he says it is pointless to talk about ‘value’ simply because “value is not part of the world.” He made similar points about some philosophical discussions.
The relevance to the mathematical logic discussed here is that he said logic is essentially tautologous - different ways of saying the same thing , conveying “no substantial information about the world.”
Wittgenstein has been much criticised for starting a trend in philosophy - an obsession with word games. He defended his position by saying he was simply trying to emphasize what we can and cannot meaningfully talk about. This point is reiterated in the famous closing sentence of the Tractus - “Whereof one cannot speak, thereof one must be silent.”
Whilst there may be some zen ways of thinking that 1+1 does not necessarily equal 2. I was thinking of purely mathematical ways. Now I’ve read this before, but can’t remember the details, but someone basically proved that 1+1=0 (or maybe it was 3), using mathematicla theory. Or I might be remembering it all wrong, and it’s a load of bullshit - it was a long time ago. The point I was getting at was about ‘fact’ not being all it’s cracked up to be, and in “fact”, not being anything at all really. I mean take Newtonian physics, I nice set of laws and rules that llow us to build bridges and calculate the trajectories of spaceships and stuff. Then Einstein and them Quantam physics guys go and prove a lot of these laws wrong. But the bridges don’t fall down. What was going on. Are these ‘laws’ facts? Is ‘the sun orbits the earth’ a fact?
[quote=“miltownkid”]I was talking with and older and wiser (and grumpier ) friend of mine earlier today about this 1+1 thing. We had a nice talk, then he sent me this email later on. I hope someone enjoy’s it as much as I do. (he asked to be reffered to as Dr. Enura ezz)[quote=“Dr. Enura ezz”]Does 1+1=2?
This depends on if you are capable of talking from your ass. You see if you can speak from deep down where the shit lines up to parachute into the toilet, you can create your own reality where those so called laws of
science and nature no longer apply and perhaps never existed. You might ask,“isn’t reality just what is real?” The answer is NO. Those who can speak from the sphincter live in a world entirely or partially (depending on their reality) of their own creation. Therefore, 1+1 does not have to equal 2. 1+1 can equal a Toyota Corolla. Rain may no longer be called rain. It can be called sazbach, and it’s no longer wet. It’s jizzy.
Of course, it no longer contains the properties of rain or water for this is my reality. It all depends on what reality you subscribe to (or in technical terms how loud the voice in your ass is). Most people subscribe to basic cable. I on the other hand use pay per view. So, in my reality 1+1 does not equal 2. It equals Jennifer Lopez, Sandra Bullock, and myself in a wild bi-sexual sexfest. You dig? You might ask,“Does talking from your ass hurt?” For some it might but for the most part it only irritates those around them. Those around you might think you are pretentious, dillusional, or just plain crazy. However, that is their reality and their rules don’t apply to you- neither does gravity for that matter.[/quote]
I don’t want to convice anyone that 1+1=2 (or anything for that matter), I think I just had a natural reflex to keep people from getting dumber. Maybe this is what’s missing from the conversation. There are fatcs and beliefs, when people start spreading their beliefs as facts things get clouded.
How can you separate a fact from a belief? Maybe that’s up to the individual. Forget trying to proof 1+1=2, how do you proof God exists (or doesn’t)? (just an example, I’m not trying to start up something else). I’ll stop there.[/quote]
I completely agree with your point on seperation of Fact from Belief. This is important & may seem simple but as we have demonstrated is incredibly difficult.
Regarding Dr Ezz. He may well be older & grumpier but I find little wisdom in his words. Basically he is saying that is you do not agree that 1+ 1 = 2 then you are talking out of your ass. This does not seem like much of an argument to me.
You could apply the same words but replace 1+1 = 2 with The earth is Flat. Or that Blacks committ more crime. All he provides is his opinion & that any one with an alternative opinion talks out of thier ass.
there is a mathematical proof to show 1+1=2, but none of us seem to be mathematically inclined enough to prove it here, and the rest of us wouldn’t be able to understand it anyways.
mathematical proofs (e.g. geometry proofs, most of which require certain assumptions) are only a certain kind of fact.
this is separate from the kinds of “fact” and “opinion” that is being expressed here.
btw, there was a post above about some old story about the statement “I always lie.” Comes from an old greek philosophical argument by some famous Greek dude who talked about “there was a man from Mino or some island where everyone lies. the man tells us ‘statement a’ and statement b’.” which is the truth and which a lie and paradoxes blah blah to prove a point about logic or relativity of truth i think. i guess i could look it up if anyone cares.
My final thoughts (or rather somebody smarter than me) on Fact vs opinion & excluding mathematics:
“The whole problem with the world is that fools & fanatics are always so certain of themselves but wiser people so full of doubts”: Bertrand Russell (1872-1970)
2.Qn: How long is a minute ?
Ans: It depends which side of the toilet door you are on.
) read the book.
)