Chiki Posted April 19, 2013 Share Posted April 19, 2013 Prove 1+1=2. Quote Link to comment Share on other sites More sharing options...
Darros Posted April 19, 2013 Share Posted April 19, 2013 let 1 = x x + x = 2x As stated before, x = 1, so 2x must equal 2 2x = 2(1) 2x = 2 We stated earlier that x + x = 2x x + x = 2 As stated before, x = 1, so 1 + 1 = 2 Quote Link to comment Share on other sites More sharing options...
Chiki Posted April 19, 2013 Author Share Posted April 19, 2013 That's middle school algebra proof lol Quote Link to comment Share on other sites More sharing options...
Darros Posted April 19, 2013 Share Posted April 19, 2013 It didn't say prove using a specific method though! D: I refuse to use induction I hate induction it is the very evil. Also can you even solve this with induction? I don't think so lol Quote Link to comment Share on other sites More sharing options...
Freohr Datia Posted April 19, 2013 Share Posted April 19, 2013 Lol you said prove it and nothing else you goof xb Quote Link to comment Share on other sites More sharing options...
Zerker Posted April 19, 2013 Share Posted April 19, 2013 Hold up a finger in one hand. Hold up another in the opposite hand. Move them together. DONE HERE Quote Link to comment Share on other sites More sharing options...
Esau of Isaac Posted April 19, 2013 Share Posted April 19, 2013 Prove 1+1=2. 1+1=2. Phew. Someone get me a towel that was hard work. Quote Link to comment Share on other sites More sharing options...
Elieson Posted April 19, 2013 Share Posted April 19, 2013 1+1=2 subtract 1 from both sides of the equation 1=1 Again 0=0 Wait I just broke it. Quote Link to comment Share on other sites More sharing options...
BBM Posted April 19, 2013 Share Posted April 19, 2013 Serious answer because I'm bored: you can't actually prove that x + x = 2x without using 1 + 1 = 2. x + x = 2x only because: x + x = x(1) + x(1) (unitary property) x + x = x(1 + 1) (distributive property) x + x = 2x There's no way to "prove" that 1 + 1 = 2; that's just how the number system was defined. Quote Link to comment Share on other sites More sharing options...
OrangeCrush980 Posted April 19, 2013 Share Posted April 19, 2013 Use the rule of addition Quote Link to comment Share on other sites More sharing options...
Chiki Posted April 19, 2013 Author Share Posted April 19, 2013 Serious answer because I'm bored: you can't actually prove that x + x = 2x without using 1 + 1 = 2. x + x = 2x only because: x + x = x(1) + x(1) (unitary property) x + x = x(1 + 1) (distributive property) x + x = 2x There's no way to "prove" that 1 + 1 = 2; that's just how the number system was defined. Yes there is. :< in a book called Prinicipia Mathematica a man called Russell took 300 pages to prove it. Quote Link to comment Share on other sites More sharing options...
LeThiAnh Posted April 19, 2013 Share Posted April 19, 2013 Yes there is. :< in a book called Prinicipia Mathematica a man called Russell took 300 pages to prove it. Math: You gotta expect silly people to make a short proof extremely long. Next thing you know, they prove that 1+1=0 is true. ....Wait. Quote Link to comment Share on other sites More sharing options...
Fruity Insanity Posted April 19, 2013 Share Posted April 19, 2013 You have one cookie. You get one more cookie. Now you have zero cookies. ...Don't look at me like that! I didn't eat them! Nope, not at all. Quote Link to comment Share on other sites More sharing options...
peener weener Posted April 19, 2013 Share Posted April 19, 2013 the simpler it seems, the harder it is to actually prove usually Quote Link to comment Share on other sites More sharing options...
Darros Posted April 19, 2013 Share Posted April 19, 2013 Math: You gotta expect silly people to make a short proof extremely long. Next thing you know, they prove that 1+1=0 is true. ....Wait. Silly, everyone knows 1 + 1 = 10 Quote Link to comment Share on other sites More sharing options...
Mikethfc Posted April 19, 2013 Share Posted April 19, 2013 (edited) Maths : You gotta expect silly people to make a short proof extremely long. Next thing you know, they prove that 1+1=0 is true. ....Wait. Well, if you're working in modulo 2 then yes. Yes there is. :< in a book called Prinicipia Mathematica a man called Russell took 300 pages to prove it. Edited April 19, 2013 by Mikethfc Quote Link to comment Share on other sites More sharing options...
BBM Posted April 19, 2013 Share Posted April 19, 2013 It's sort of a dumb proof though, because it still depends on the definition of two. Quote Link to comment Share on other sites More sharing options...
Chiki Posted April 19, 2013 Author Share Posted April 19, 2013 Math: You gotta expect silly people to make a short proof extremely long. Next thing you know, they prove that 1+1=0 is true. ....Wait. You think x + x = 2 is proof that 1 + 1 = 2? Quote Link to comment Share on other sites More sharing options...
Shin Posted April 20, 2013 Share Posted April 20, 2013 Silly, everyone knows 1 + 1 = 10 Fool! It's really 11! No wonder you're so bad at maths! Quote Link to comment Share on other sites More sharing options...
Jaybee Posted April 20, 2013 Share Posted April 20, 2013 GODDAMN Quote Link to comment Share on other sites More sharing options...
Darros Posted April 20, 2013 Share Posted April 20, 2013 Fool! It's really 11! No wonder you're so bad at maths! But I was using the magical BINARY system. Quote Link to comment Share on other sites More sharing options...
Narga_Rocks Posted April 20, 2013 Share Posted April 20, 2013 Is this a serious question you were asked for homework? How do they expect you to prove something like that? It's only true because we have defined the number system to be linear with 0, 1, 2, 3, 4, etc being the values for equivalent distances and addition to be combining two values in such a way as to start at one spot of the number system and move right or left a certain number of "spots" based on the value of the other number you are adding. Or alternatively, taking the value of a + b as the value of a and the value of b lumped together and then count up the number system until you reach the answer. Thus if I have an apple each in my left and right hands (1+1) and I throw them into the same pile, I can now count that I have 2 apples because we've defined the number system that way. Are they looking for pages of proof of 1+1=2 or something? It sounds a lot like asking to prove that green is green when it's only green because we decided to name whatever we see with that wavelength green. Quote Link to comment Share on other sites More sharing options...
Redwall Posted April 20, 2013 Share Posted April 20, 2013 (edited) I think he made the topic as a joke of sorts since another user had made a thread about an actual homework problem. But Olwen is serious about the proof: http://en.wikipedia.org/wiki/Principia_Mathematica#Quotations Edited April 20, 2013 by Redwall Quote Link to comment Share on other sites More sharing options...
Narga_Rocks Posted April 20, 2013 Share Posted April 20, 2013 I think he made the topic as a joke of sorts since another user had made a thread about an actual homework problem. But Olwen is serious about the proof: http://en.wikipedia.org/wiki/Principia_Mathematica#Quotations So it is, basically, by definition 1+1=2. Quote Link to comment Share on other sites More sharing options...
Chiki Posted April 20, 2013 Author Share Posted April 20, 2013 By definition, a successor of a number is a number. So the successor of 0 is one, the double successor of 0 is 2, and so on. Also by definition, a number plus zero is itself. That's where the definitions end, and 1+1=2 isn't by definition true. If you take the above axioms you'll find that 1+1 and 2 are both the double successors of 0, which proves it. You can prove any addition and subtraction and multiplication this way. Quote Link to comment Share on other sites More sharing options...
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