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viktor
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I'm doing assignment which concern the 20 greatest equation, but i can't figure out why 1+1=2 is in it?
Why do you think 1+1=2 is an equation?
Poop-Loops said:If you have to prove to yourself that 1 + 1 = 2, then maybe you should find a different field to work in.
Poop-Loops said:If you have to prove to yourself that 1 + 1 = 2, then maybe you should find a different field to work in.
fasterthanjoao said:Maybe you should try it..
Poop-Loops said:If I have one carrot:
And then add another carrot:
I now have TWO carrots:
f95toli said:The problem is that this is only an argument (albeit a very plausible one), not a proof. It would be "good enough" in most sciences but not in mathematics.
That's a 'tude much more open to learning something new than 'wtf is wrong with you'.Poop-Loops said:That's a lot of jargon there. I wish I understood it. :(
f95toli said:Well, the proof can be found in Russell/Whiteheads Principia Mathematica (Yes, that really is the name of the books) and it is far from trivial.
1+1=2 is a very fundamental equation in all work on the foundations of mathematics.
The Pythagoras theorem is on it:Asphodel said:I don't know, but if the Pythagorean theorem isn't on it then it's a sucky list.
From anyone else, I would think that was a foolish post. From arildno, I think I am missing something! Arildno, I think 1+ 1= 2 is an equation because it has an "=" in it! What am I missing?arildno said:Eeh?
Greatest equations??
Why do you think 1+1=2 is an equation?
Yes, you should be working in mathematics!Poop-Loops said:If you have to prove to yourself that 1 + 1 = 2, then maybe you should find a different field to work in.
That's a statement about carrots, not about mathematics!Poop-Loops said:If I have one carrot:
And then add another carrot:
I now have TWO carrots:
Now this I agree with. Arildno, "wtf"?Also, for those actually debating whether 1 + 1 = 2 is an equation: wtf is wrong with you? There is an EQUALS sign right there. That is what defines an equation, no?
Asphodel said:You can't construct an ordered field of integers without defining their order, which means that for any integer you should be able to trivially say what the next one is.
CaptainQuasar said:Just as a note, defining an order is not the same thing as defining a property of addition.⚛
John Creighto said:2 is a definition. You can only prove 1+1=2 after you define what 2 is. It is kind of like proving God.
CaptainQuasar said:What I meant is that you might define something like a http://mathworld.wolfram.com/PartialOrder.html" and then you can say that one object of the set is more or less than another but you don't necessarily have any operation equivalent to addition.⚛
http://en.wikipedia.org/wiki/Peano_axioms#Arithmetic== Arithmetic ==
The Peano axioms can be augmented with the operations of addition and multiplication and the usual total (linear) ordering on ''N''. The respective functions and relations are constructed in second-order logic , and are shown to be unique using the Peano axioms.
Addition is the function + : ''N'' × ''N'' → ''N'' (written in the usual infix notation), defined recursively as:
[tex]\begin{align}
a + 0 &= a ,\\
a + (S (b)) &= S (a + b).
\end{align}[/tex]
Poop-Loops said:That's a lot of jargon there. I wish I understood it. :(
OmCheeto said:I disproved this at the age of 4, when my sister came home from her third grade class, all excited, and tried to teach me that when you have one pie and take away two pies, you end up with minus one pie.
CaptainQuasar said:Oh, wait… nevermind… that would violate Newton's Law of Conservation of Pie.⚛
CaptainQuasar said:John Creighto, the thing you quoted is talking about a set with a total order on it, not a partial order. Those are different things.
If you tried to do a square-peg-in-a-round-hole type fitting of real number arithmetic into a partially ordered set the Cartesian product ''N'' × ''N'' → ''N'' wouldn't necessarily be true. You're to be commended for your cutting-and-pasting-from-Wikipedia skills, though.⚛
John Creighto said:I don't believe I said that you could create addition from a partial order.