3^0=1 and 4^0=1 can't both be true using your argument Just like any number raised to the 0 is 1, 1 plus any number is 3 I can prove this like this; Well, if you want an actual formal proof, see the metamath proof of 22=4 (11=2 is boring because that's how it defines 2) (11=2 is boring because that's how it defines 2)The later theorem alluded to, that $11=2$, appears in section $\ast102$, considerably farther on I wrote a blog articlea few years ago that discusses this in
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Can 1 plus 1 not equal 2-X 1/2 1/2 = 2/2 1/2 x 1/2 1/2 leaves x and 2/2 1/2 is 1/2 which means we end up with x = 1/2 Therefore, the answer to "What plus 1/2 equals 2/2?" is as follows 1/2 It is always good to doublecheck your math to make sure you did it right When we entered 1/2 for x in this equation x 1/2 = 2/2, we get the following true equationThe second one doesn't work, though, and requires broken math on the part of the individual If 99(repeated) = 10x, then dividing to find x means 9 = 9x isn't true 1
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If all of the symbols take on their most common mathematical meaning, then 11 always equals 2 PRO should win this debate easily, though, because there are a number of contexts in which this isn't true, and he never specifiedStep Justification Check a = b Given Check ab = b^2 Multiply both sides by b Check ab a^2 = b^2 a^2 Subtract a^2 from both sides There is only one illegal step in this proof Click on the button next to the step you think is invalid The correctness of your choice will beThe following is a "proof" that one equals zero Consider two nonzero numbers x and y such that x = y Then x 2 = xy Subtract the same thing from both sides x 2 – y 2 = xy – y 2 Dividing by (xy), obtain x y = y Since x = y, we see that 2 y = y Thus 2 = 1, since we started with y nonzero Subtracting 1 from both sides, 1 = 0
Ments that are already proved and progresses one step at a time until the goal is achieved A defect of synthetic proofs is that they don't explain why any step is made Proof Let t be any number in an interval 1;1 1 n Then 1 1 1 n 1 t 1 Therefore Z 11 n 1 1 1 1 n dt Z 11 n 1 1 t dt Z 11 n 1 1dt The rst integral equals 1 n1We use only the usual field axioms for the real numbers First we prove an intermediate result Subtract 0 × 0 from each side to get 0 = 0 × 0 Now we are ready for the final kill Add 1 to each side to get 1 = ( − 1) × ( − 1) The Law of Signs ( − x) ( − y) = x y isn't normally assumed as an axiom if 11=3 and 12=3 can't both be true then;
In the case of the square root the nonnegative value is the principal value, but there is no guarantee that the square root given as the principal value of the square of a number will be equal to the original number (eg the principal square root of the square of −2 is 2)The proof for 11=2 is kind of interesting, and it's not very complicated First, you need to create the counting numbers, like so Suppose we have a set of objects, not sure yet how many or what they are; If you're looking for a proof from first principles, I suppose we can expand the argument to this Any symbol that is defined is equal to its definition The symbol "2" is defined as "11" Therefore, 11=2
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Or if we take 1 drop of water and "add" it to 1 other drop of water We still end up with just 1One value can be chosen by convention as the principal value; One shot is 15 ounces 100 shots x 15 ounces = 150 ounces of beer in 100 minutes Each Beer is 12 ounces 150ounces divided by 12 ounces = 125 Beers How many beers equal a vodka shot?
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Proof that 1 = 2 (see below) What You Do Show your teen the proof Ask her to tell you which step is invalid She should determine both which number is wrong, and why Help her keep going until she understands the answer The Proof that 2 = 1 1) a = b 1) Given 2) a 2 = ab 2) Multiply both sides by a 3) a 2b 2 = abb 2 3) Subtract b 2 fromProof that zero is less than one In this note we will prove that 0 < 1 In order to do so we rst need a lemma Lemma For any real number x we have x2 0 Proof We will consider two cases x 0 and x < 0 In the rst case x 0 we have x2 = xx 0 0 by (O5) = 0 by x11 #4= 1, factorial notation, zero factorial equals one, zero factorial proof
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12 Proof by induction 1 PROOF TECHNIQUES Example Prove that p 2 is irrational Proof Suppose that p 2 was rational By de nition, this means that p 2 can be written as m=n for some integers m and n Since p 2 = m=n, it follows that 2 = m2=n2, so m2 = 2n2 Now any square number x2 must have an even number of prime factors, since any prime1 cross times left parenthesis 1 plus 1 right parenthesis equals fraction numerator 1 left parenthesis 1 plus 1 right parenthesis left parenthesis 1 plus 2 right parenthesis over denominator 3 end fraction Response Feedback Student shall know how to proof by mathematical induction and use mathematical induction to prove recurrence relation Start with the following simple equation $$a = b$$ (step 1) Multiply both sides by $b$ $$ab = b^2$$ (step 2) Subtract $a^2$ from both sides and factorize $$ab a^2 = b^2 a^2$$ (step 3) $$a(ba) = (ba)(ba)$$ (step 4) Simplify and add 1 to both sides $$a = b a$$ (step 5) $$a 1 = b a 1$$ Now since $a = b$ (the starting point of this proof), we can write this as $$a 1 = 2a 1$$ And in the case where $a = 1$, we have $$1 1 = 2 1$$ So, therefore, $$1 1
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Here is a quick demonstration of what can go wrong when you violate the rules of mathematics 1 Let and 2 Now this means that 3 If we multiply both sides by we get 4 If we then subtract from both sides we would have 51/2 1/2 = 1 How did we solve the problem above?111=1 is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to Amazoncom Occasionally I receive products in exchange for a review or giveaway post These posts are always labeled as reviews and/or giveaways
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Proof that one equals two Given a = b Invalid?Given 2) X^2=XY ;Substitute X for Y, by equation 1 7) 2=1 ;
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This image was sourced and then altered from the NASA image archive The chimpanzee pictured was named Ham the Astrochimp He was a brave space pioneer and proved to NASA that astronauts would be able to survive space travel This post requires familiarity with complex numbers, in particular \\( i = \\sqrt\{\1\}\\\), and \\( i^2 = \1\\\) Proof that 1 1 = 1 Not 2!?!And good news for Verizon;
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It has finally has a proof that $0002 equals 0002¢ Can you hear me now?Divide both sides by Y Proof that 2 equals 1 « First ← Prev Index Next → How to "Prove" That 2 = 1 Let's begin our journey into the bizarre world of apparently correct, yet obviously absurd, mathematical proofs by convincing ourselves that 1 1 = 1 And therefore that 2 = 1 I know this sounds crazy, but if you follow the logic (and don't already know the trick), I think you'll find that the "proof" is pretty convincing
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1=2 A Proof using Beginning Algebra The Fallacious Proof Step 1 Let a=b Step 2 Then , Step 3 , Step 4 , Step 5 , Step 6 and Step 7 This can be written as , Step 8 and cancelling the from both sides gives 1=2 See if you can figure out in which step the fallacy lies11=3 So, 1=31 1=2 12=221 Plus 1 Equals 2 Proof The following image below is a display of images that come from various sources The copyright of the image is owned by the owner, this website only displays a few snippets of several keywords that are put together in a post summary To find out more complete and clear information or images, you can visit the source
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I saw my first proof that one equals two when I was in seventh grade algebra I've been collecting them ever since Click here to see the errors in these "proofs" Go Back to my Home Page Does 1 = 2?1=2 A Proof using Complex Numbers This supposed proof uses complex numbers If you're not familiar with them, there's a brief introduction to them given below The Fallacious Proof Step 1 1/1 = 1/1 Step 2 Taking the square root of both sides Step 3 Simplifying Step 4 In other words, i/1 = 1/i Step 5 Therefore, i / 2 = 1 / (2i),2=1 a = b a 2 = ab a 2 – b 2 = ab – b 2 (ab) (ab) = b (ab) a b = b 2b = b
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Maybe, if the context of the request for a proof was a legal or scientific setting (or if one's philosophy was Brouwerian or Quinean) for example, then a proof might involve showing things like XX and OO, in order to show that 1 1 = 2 was very plausible, was highly probableWhen we add two fractions, such as 1/2 1/2, we make sure that the two denominators are the same and then we simply add the numerators In cases where the denominators are not the same, we find the lowest common denominator and adjust the fractions to keep them intactThey are just distinct things Now define a succession operation that maps any object in the set to another one, uniquely
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Several years ago, while traveling with coworkers, the subject of ( that's 9 with a bar over it, or 9 repeating infinitely ) being equal to 1111=1 is a participant in the Amazon Services LLC Associates Program, an affiliate advertising program designed to provide a means for sites to earn advertising fees by advertising and linking to Amazoncom Occasionally I receive products in exchange for a review or giveaway post These posts are always labeled as reviews and/or giveaways What is 4 plus 1 plus 4 plus plus 3 plus 8 plus 1 plus plus 6 plus 1 equals 2 plus plus 4?
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Multiply both sides by X 3) X^2Y^2=XYY^2 ;So roughly 1 shot equals one beer Depends on the beer though 12 oz of beer has approximately the same amount of alcohol as 15 oz of vodka or othe distilledCancel out (XY) term 6) 2Y=Y ;
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A formal proof that 11=2 Some related reading The table below gives a proof of 11=2 based on the proof system described in Formal proofs of Arithmetic Since 1 and 2 don't occur as basic symbols of that system, we need to define them as 0' and 0'', so the statement to be proved is 0'0'=0'' Remember that proofs in this sense are just about manipulating symbols The derivative of x 2 is equal to 2x, and the derivative of x is equal to 1 So we have the following 2x = 1 1 1 (x times) The sum of x terms of 1 is x Therefore, we have 2x = x If we take x = 1, we get a strange result 2 = 1 Clearly this is a mistake! One plus One equals One M plus E equals ME Flip the equation and ME becomes WE One plus One equals One It's been said, One can not solve the problems of this world, with the same thinking that created the problems Change your mind, to change your reality I woke up this with this simple truth running through my Dreamtime Spirit
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1st Proof x = 1 set x equal to 1 x 2 = x multiply both sides by x x 2 1 = x 1 subtract 1 from both sides (x 1)(x 1) = x 11 = 2S, resulting in S = 1 / 2 The same conclusion results from calculating −S, subtracting the result from S, and solving 2S = 1 The above manipulations do not consider what the sum of a series actually means and how said algebraic methods can be applied to divergent geometric series Still, to the extent that it is important to be able to bracket series at will, and that it is more importantFactor 5) XY=Y ;
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Got these explanations that apparently 'disprove' that 11=2 from a philosopher dude If we have 1 rabbit and put it with 1 other rabbit, after a few months, we may end up with 3 or more rabbits! Explanation 3 We can also use the following pattern We know that which means that Dividing both sides of the equation by , we have Using this fact, we can check the following pattern Now, we go to As we can see from the 3 examples, 8 comments 0!2 Equals 1 Proof What is wrong with the following proof?
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Put on your thinking cap for this one 1) X=Y ;But every step seemed valid So here's the puzzle can you find the mistake in the proof? $1 = 100¢ = (10¢) 2 = ($010) 2 = $001 = 1¢ So that's it, 1 dollar is actually equal to 1 cent!
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Subtract Y^2 from both sides 4) (XY)(XY)=Y(XY) ; The theorem above, $\ast54\cdot43$, is already a couple of hundred pages into the book (Wikipedia says 370 or so);(And of course all this is just an April Fool's joke
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3(3m 2 4m 1) 1 So we can write n = 3k 1 for k= 3m2 4m 1 Since we have proven the statement for both cases, and since Case 1 and Case 2 re ect all possible possibilities, the theorem is true 12 Proof by induction We can use induction when we want to show a statement is true for all positive integers nThis video proves that 11=3 (one plus one equals three)And you can certainly impress your math teacher with these tricksAlthough each method has a mistakeProof that 1=2 Paradox It official 1=2 And here is the proof (1) X = Y Given (2) X 2 = XY Multiply both sides by X (3) X 2 Y 2 = XY Y 2 Subtract Y 2 from both sides
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