how do you prove that 1=2,  logic answer needed with proof.?
456169
There are many proofs but with fallacies. Please visit:\nhttp://www.math.toronto.edu/mathnet/falseProofs/first1eq2.html\n\nhttp://www.math.toronto.edu/mathnet/falseProofs/second1eq2.html
863581
You have a couple of typos, I think.  As for the "proof", dividing by x - y is dividing by zero.  That is a no-no.  (In other words, a * 0 = b * 0 does not imply a = b.)
798197
LOL\n\nI can follow you up to n+1=2, what's 2n?\n\nn+1=2  so  n=2-1  so  n=1  so  2n=2
471450
weezy is on the right track, that glow1989 is on the right track.  For everyone who thinks that writing 1+1=2 is so obvious that it constitutes a self-contained proof of itself(!)... if you undertake a serious study of mathematical proof, you might find that 357 pages is a good length for a quick introduction to the ideas that are involved in considering questions in this area.  Of course, I am talking about actually UNDERSTANDING something - very different to simply passing an exam, regardless of the 'level' of maths you are enrolled in.\n\nYes, as you mentioned, this is a hard question.  'Proving' that 1+1=2 is not as simple as it sounds, because of the inherent question of what we mean by 'prove'.  You might have noticed that some proofs you have used depend on other proofs, which in turn depend on other proofs, ... which ultimately rest on a handful of axioms.  It is the nature of operations that are allowed by any axiomatic system, that determine the characteristics of mathematical problems that can be said to be SOLVABLE.  It is no small task to understand the axioms that underlie our systems of mathematics.  For example, maths students learn: that division by zero is undefined; that any object raised to a null power is equal to unity; some differences between rational and irrational numbers; what we mean when we consider objects to exist in 'sets'; and so on.  Those who consider themselves to be excellent students are usually able to list these rules in rapid-fire style.  But if we are asked to 'prove' why those rules are the way they are, the questions start to seem fuzzy, and you typically run out of convenient formulas to rely on.  You could easily write 357 pages just to explain what you actually MEAN by the numbers 1 or 2, without worrying about the definition of the addition operation!  As usual, people might do better to stop and consider what the question is asking before booting in a smug answer.\n\nLook into Hilbert's Problem (David Hilbert - German mathematician), which was a more workable and compact form of a proposal by Russell and Whitehead to formalise mathematics on a general basis, according to well-established axioms and procedures.\n\nOther notable mathematicians to work in this area were Alan Turing, Alonzo Church (look for Church's Lambda Calculus), Emil Post, and the brilliant Kurt Gödel.  In more recent decades, look for Gandy (1988) and of course many others.\n\nLol, molawby is spot-on.  I wish he'd posted b4 me... would've saved me a bit of typing.  If all you need to do is learn to sing the right song, to pass your exams and get the job that stipulates that you need to have completed such-and-such a course, then you don't have to worry about any of this.  Of course, that doesn't mean you have to dismiss it either.  But if you are chasing a deeper understanding, it probably does take the 20 yrs, and you won't necessarily get paid for it, heheheh.\n\nFor bedside reading, I suggest Roger Penrose etc...
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.
266936
Counterexample: 1\n\nJay's proof is false because x(x-1) = 0 just says that x could be either 1 or 0 to satisfy that equation. x was 1 in that case. It does not mean that 1=0.\n\nJZ-LP's proof is false because you can't say let 1=0.\n\nBianca is just plain wrong.
717483
1\nbecause u have mentioned that 1=5 so 5=1 and it cant = 9
806805
You can prove it by induction.\n\nIt is obviously true when n = 1.\n\nInduction pypothesis:  Suppose it is true for n\n\nWe need to show  is true for (n+1).\n\nDoes 24 divide (5^(2*(n+1))-1))?\n\nWe can rewrrite this as:\n\n25*(5^2n)-1  Subtract 24 from this to get 25*(5^2n)-25 \n\nThis is just equal to 25*(5^2n)-1).\n\nThis has to be divisible by 24 -- since one of the factors is (5^2n)-1) and our induction hypothesis says that it is.  \n\nAdd 24 to it and we get something that is also divisible by 24 -- but it is (5^(2*(n+1))-1)) -- so our induction is done.
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.
328795
1 + 1 = whatever you want to make.
252884
"1+1" without equals is 11 but with equals as "1+1=" is equivalent to 2
732898
ab=a+b\nab-a-b+1=1\n(a-1)(b-1)=1\na=(1/(b-1))+1\nIf a is not 1 and b is not 1, then you can find a if you know b and vice versa. Therefore, if a is anything other than 1, you can find b that works and vice versa.
46798
if (1/x) + 2= (c/2)\n--------------------------------\n\n1/x = (c/2) - 2\n----------------------\nx = 1/((c/2) - 2)\n       (OR)\nx = ((c/2)-2)^-1\n-----------------------
637914
1=1. Simple yet important.
1153023
It is really surprising that there are still people who think they have a PROOF for statements like 1=2, 1=0, etc.\nFirst they should UNDERSTAND what is a PROOF.\n\nPROOF is a sequence of logically correct steps. If ONE of your step is wrong then it is NOT called a proof.\n\nI think these people should go back to Primary schools and LEARN the fundamentals.
469247
A = A\n\nThis is one.
864701
Prove by induction.\n\nWhen k=1, then (n+a)^1 = n+a = Θn, true\n\nAssume true for k.\n\nFor k+1,\n(n+a)^(k+1) = (n+a) * (n+a)^k = Θn * Θ(n^k) = Θ(n^(k+1))\n\nTherefore it holds for all k>0