square173205 Posted November 9, 2007 Share Posted November 9, 2007 Is 1+1 always 2? I tried to prove that 1+1 is not always 2 with applying Goedel's incompleteness theorem as; http://hecoaustralia.fortunecity.com/incompleteness/incomplete.htm Link to comment Share on other sites More sharing options...
insane_alien Posted November 9, 2007 Share Posted November 9, 2007 why not post it here instead of continually linking to your own site. also, if you used the search function you would find that we have been over this several times. Link to comment Share on other sites More sharing options...
Klaynos Posted November 9, 2007 Share Posted November 9, 2007 Is the definition of 2 not that it is always 1+1? Link to comment Share on other sites More sharing options...
uncool Posted November 9, 2007 Share Posted November 9, 2007 Is the definition of 2 not that it is always 1+1? Not always; in an axiomatic definition of the integers, you can prove that; it is defined in that case as the least integer greater than 1. =Uncool- Link to comment Share on other sites More sharing options...
Country Boy Posted November 9, 2007 Share Posted November 9, 2007 And in what system is that not DEFINED as 2? Link to comment Share on other sites More sharing options...
uncool Posted November 10, 2007 Share Posted November 10, 2007 And in what system is that not DEFINED as 2? 2 is sometimes defined as 1+1, and sometimes as the successor of 1. The two must be proven equivalent. Otherwise, I don't think I understand your question... =Uncool- Link to comment Share on other sites More sharing options...
square173205 Posted November 10, 2007 Author Share Posted November 10, 2007 Is the definition of 2 not that it is always 1+1? Yes, it's a definition. But it might be necessary to verify that definition is well-defined. Otherwise we could define 1+1=3 (it's obviously not well-defined, though.) Link to comment Share on other sites More sharing options...
DivideByZero Posted December 2, 2007 Share Posted December 2, 2007 I don't understand why one would assume 1 and 1 wont equal 2. If you have 1 apple and 1 plum, you have 2 fruits. I don't know.. maybe I'm overlooking something obvious. Btw this is my first post so Hello SFN!! Link to comment Share on other sites More sharing options...
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