Explain that 1=2 in mathematics?
81246
Let A = 1 - 1/2 + 1/3 - 1/4 + 1/5 - ... \n\n(Note that A is equal to ln 2)\n\nA = (1 + 1/3 + 1/5 + ...) - (1/2 + 1/4 + 1/6 + ...) \n\nA = (1 + 1/3 + 1/5 + ...) - 1/2 (1 + 1/2 + 1/3 + ...) \n\nA = (1 + 1/3 + 1/5 + ...) - 1/2 (1 + 1/3 + 1/5 + ...) - 1/2 (1/2 + 1/4 +1/6 + ...) \n\nA = 1/2 (1 + 1/3 + 1/5 + ...) - 1/2 (1/2 + 1/4 +1/6 + ...) \n\nA = 1/2 (1 - 1/2 + 1/3 - 1/4 + 1/5 - ...) \n\nA = 1/2 A \n\n1 = 1/2 \n\n2 = 1 \n\n\n----------------------------------------------------------\nSpoiler - do not read below until you try to find the error\n-----------------------------------------------------------\n\nThe problem here is that the sequence, although it converges is said to be "conditionally convergent". The sequence as stated in the first line is considered to converge, by when split apart into even and odd members, has been transformed into an infinity minus infinity, thus it is no longer considered to converge.\n\nI used to play with these types of proofs in high school, and this was by far my favourite!
705951
b) 2/X, since x/2 * 2/X = 1, which is the definition of the multiplicative inverse.
990578
Our society uses base 10; thus, 1 + 1 = 2.  Try converting your 1 + 1 mathematical sentence to another base and see if you can find one that will equal 3~here are the directions to convert bases~\nhttp://www.britannica.com/eb/article-205799
166763
1+1=2 is an axiom - something that we consider being true without proving it.
469247
A = A\n\nThis is one.
1023705
2 + 2 / 2 =\n2 + 1 = 3
355004
1. a = b + 1 (Given, let a and b be two numbers such that a = b + 1)\n\n2. (a-b)*a = (a-b)*(b+1)\n\n3. a^2 - ab = ab + a - b^2 - b\n\n4. a^2 - ab - a = ab + a  - a - b^2 - b\n\n5. a*(a - b - 1) = b*(a - b - 1)\n\n6. a = b\n\n7. b + 1 = b\n\n8. Therefore, 1 = 0
200519
+/- 1\n\nThe answer is not 1, because -1 * -1 = 1 also.
369170
same as everywhere\n1+1=2\n2+2=4
297621
In boolean logic, a rule says: A + A = A (see: http://en.wikipedia.org/wiki/Boolean_algebra if you don't believe)\n\nThus if A equals to 1:\n1 + 1 = 1\n2 = 1\n\nNOTE: Wikipedians uses v and inverted v to represents the use of AND and OR logic, I am used to use + and . (multiplication dots), and I think this is the more correct one than wikipedians, since the equation being done here is more in boolean algebra and not only boolean logic
646877
actually, 1+1 isn't always 2, only in the collections N={0,1,2...}; Z={...,-2,-1,0,1,2...}; Q (fractions)\n\nwhen you have other collections, like Z 2, you have only two numbers 0 and 1:\n0 = every number that has rest 0 when it is devided by 2 (like 2,4,6,-2,...)\n1 = every number that has rest 1 when it is devided by 2 (like 3,5,6,-1,...)\nWhen you now do 1 + 1 you ectually add a number of collection 1 to another of collection 1, by example 5 and 15. 5 + 15 = 20 and 20 is a number of the collection 0 (20/2=10 rest 0)\nNow you can say 1 + 1 = 0
10761
this is a common "proof" that is often bandied about, even though it's wrong.  \n\nLet a=b. \n\nmultiply by a:\na^2 = ab\n\nsubtract b^2:\na^2 - b^2 = ab - b^2\n\nfactor both sides:\n(a+b)(a-b) = (a-b)b\n\ncancel (a-b)\n(a+b) = b\n\nsubstitute a=b from the first step:\n2b = b\n\ndivide by b:\n2=1\n\nsubtract 1 from both sides\n1=0\n\n\nfortunately sanity is saved when you realize that the step where you cancel (b-a) from both sides is actually dividing by zero, since you specify beforehand that b=a.  this is not so much a proof as a mathematical fallacy.  see the link below for another, more complicated version of the same thing.
599364
x^2 + x = x(x+1)\n\nIt can be simplified to x(x+1).
357221
You are thinking of the book 'Principia Mathematica' by (Bertrand) Russell and Whitehead, written in 1913. The book was actually dedicated to putting mathematics on a logical foundation. It uses rather antiquated notation and really didn't accomplish what it intended to do, but it was a massive effort. The statement that 1+1=2 came in the middle of the second volume of the three volume set. There is a paperback version for about the first half of the first volume that is still available.
655260
2=-1=x\n2+1=x\nthere fore x =3
739421
x<1/2(x+y)<y can be proved by splitting it in two parts and proving those:\nx<1/2(x+y) is true because 1/2(x+y) > 1/2(x+x) = x\n1/2(x+y)<y is true because 1/2(x+y) < 1/2(y+y) = y
936497
To a mathematician 1 + 1=2 right. If I were using that equation in another context it could be interpreted differently. In a nutshell the quote is saying that people sometimes interpet the same one thing differently.