AdamSmith Posted March 7, 2016 Share Posted March 7, 2016 P.S. There is a more elaborate version that starts: A + B = C ...and ends: A = B Link to comment Share on other sites More sharing options...
AdamSmith Posted March 7, 2016 Share Posted March 7, 2016 Isn't the error line 3? You can't divide by zero so line 3 is only true when x-x <> 0. And that's not defined (in the real numbers at least). Yes, division by zero is the culprit. Link to comment Share on other sites More sharing options...
+ quoththeraven Posted March 7, 2016 Share Posted March 7, 2016 Does x^2 - x^2 not factor out the way it shows up there? (I can't remember how any more. Senescence!) If so, that's just a goof. The real error that allows the apparent proof that 1=2 is the division by zero. @quoththeraven, I thought you yourself pointed that out when we brought up this case a few months ago? Must have been someone else. It's been awhile since I've dealt with these types of equations, but I'm not seeing how x squared minus x squared is equal to (x+x) (x-x). It's the (x+x) that I don't understand the justification for. Doesn't this whole thing start with 0=0 (x squared minus x squared of necessity equals zero)? Link to comment Share on other sites More sharing options...
AdamSmith Posted March 7, 2016 Share Posted March 7, 2016 Must have been someone else. It's been awhile since I've dealt with these types of equations, but I'm not seeing how x squared minus x squared is equal to (x+x) (x-x). It's the (x+x) that I don't understand the justification for. Doesn't this whole thing start with 0=0 (x squared minus x squared of necessity equals zero)? The whole error is the division by an expression that equals zero. Using x for both variables is messy. Let me try to recall here the better formulation: a = b a^2 = ab a^2 - b^2 = ab - b^2 (a + b) (a - b) = b (a - b) a + b = b b + b = b 2b = b 2 = 1 Link to comment Share on other sites More sharing options...
+ Gar1eth Posted March 7, 2016 Share Posted March 7, 2016 I don't think that's the error. Line 2 is incorrect, specifically the part after the equal sign. Must have been someone else. It's been awhile since I've dealt with these types of equations, but I'm not seeing how x squared minus x squared is equal to (x+x) (x-x). It's the (x+x) that I don't understand the justification for. Doesn't this whole thing start with 0=0 (x squared minus x squared of necessity equals zero)? No it's right. It's called 'factoring the difference of (perfect) squares. See the video below. Does x^2 - x^2 not factor out the way it shows up there? (I can't remember how any more. Senescence!) If so, that's just a goof. The real error that allows the apparent proof that 1=2 is the division by zero. @quoththeraven, I thought you yourself pointed that out when we brought up this case a few months ago? Isn't the error line 3? You can't divide by zero so line 3 is only true when x-x <> 0. And that's not defined (in the real numbers at least). According to what my 10 th grade geometry teacher said (and maybe my 1st year algebra teacher the year before), all these proofs rely on dividing by zero at some point. It's usually cleverly 'disguised' so you can't always pick it out. It's also one reason why math teachers don't actually like you to say that you are 'cancelling' out factors on both sides of the equation. What you are actually doing is dividing by the factor in question. And if you know the factor is = to zero, you know you can't actually do it. Here's the reason line 2 is correct @quoththeraven. If you don't like this video-you can go from the other direction and use the FOIL (First-Outer-Inner-Last) Method to multiply (X + Y) times (X - Y) to see that it gives you (X ^2 - Y ^ 2) but you can substitute X for Y and it gives you the example above. Gman AdamSmith 1 Link to comment Share on other sites More sharing options...
+ Gar1eth Posted March 7, 2016 Share Posted March 7, 2016 FOIL ( a + b) times ( a - b) First a X a = a ^ 2 Outer a X -b = - ab Inner b X a = a X b = + ab Last b X - b = - b ^ 2 So a ^ 2 + (-ab) + (ab) - b ^ 2 = a ^ 2 - b ^2 If b = a you get the equivalent expression @AdamSmith used. @quoththeraven you are correct that the original expression is equal to zero. That's part of the trick in these proofs. Using letters instead of actual numbers, people often lose sight of that. Gman AdamSmith 1 Link to comment Share on other sites More sharing options...
instudiocity Posted March 7, 2016 Share Posted March 7, 2016 Somehow Jackhammer's Friday Funnies got hijacked by "NERD CENTRAL" TruHart1, + quoththeraven and tanman4u 3 Link to comment Share on other sites More sharing options...
+ Gar1eth Posted March 7, 2016 Share Posted March 7, 2016 Somehow Jackhammer's Friday Funnies got hijacked by "NERD CENTRAL" I'm trying to help @AdamSmith in his quest to spread enlightenment to our Forum Brethren. And sadly-sigh-this is the thanks we get. Gman + honcho, + quoththeraven and AdamSmith 3 Link to comment Share on other sites More sharing options...
+ WmClarke Posted March 7, 2016 Share Posted March 7, 2016 This thread is for funny stuff. Mathematical explanations are not funny..... they are.... ZZZzzzzzzz....... instudiocity 1 Link to comment Share on other sites More sharing options...
+ Truereview Posted March 7, 2016 Share Posted March 7, 2016 This thread is for funny stuff. Mathematical explanations are not funny..... they are.... ZZZzzzzzzz....... + quoththeraven, + WmClarke, + Gar1eth and 5 others 8 Link to comment Share on other sites More sharing options...
+ quoththeraven Posted March 7, 2016 Share Posted March 7, 2016 @quoththeraven you are correct that the original expression is equal to zero. That's part of the trick in these proofs. Using letters instead of actual numbers, people often lose sight of that. As far as I'm concerned, the whole thing could have stopped there. Here's another punny joke: Source + WmClarke and + Gar1eth 2 Link to comment Share on other sites More sharing options...
+ quoththeraven Posted March 7, 2016 Share Posted March 7, 2016 Source TruHart1 1 Link to comment Share on other sites More sharing options...
+ quoththeraven Posted March 7, 2016 Share Posted March 7, 2016 Source TruHart1, + WmClarke and + honcho 3 Link to comment Share on other sites More sharing options...
Zman Posted March 7, 2016 Share Posted March 7, 2016 TruHart1, AdamSmith and MsGuy 3 Link to comment Share on other sites More sharing options...
+ honcho Posted March 7, 2016 Share Posted March 7, 2016 This thread is for funny stuff. Mathematical explanations are not funny..... they are.... ZZZzzzzzzz....... Well, if you're willing to settle for entertaining may I suggest: AdamSmith 1 Link to comment Share on other sites More sharing options...
+ Gar1eth Posted March 7, 2016 Share Posted March 7, 2016 Source I had to look up the meaning of this joke. But I understood it when I looked it up almost immediately whereas I didn't here because there's a line missing. After the juggler asks them whether they can see him the next line is supposed to be 'What do they say in Response?'. Gman Link to comment Share on other sites More sharing options...
+ Gar1eth Posted March 7, 2016 Share Posted March 7, 2016 Gman + quoththeraven, AdamSmith, + glennnn and 3 others 6 Link to comment Share on other sites More sharing options...
Rod Hagen Posted March 7, 2016 Share Posted March 7, 2016 I remember spitting my coffee out when I read this one before school as a kid. Fantastic. AdamSmith 1 Link to comment Share on other sites More sharing options...
sincitymix Posted March 7, 2016 Share Posted March 7, 2016 I need Kurtis to sit me on his lap and explain in detailed steps this math equation mike carey and AdamSmith 2 Link to comment Share on other sites More sharing options...
AdamSmith Posted March 7, 2016 Share Posted March 7, 2016 I need Kurtis to sit me on his lap and explain in detailed steps this math equation http://www.quickmeme.com/img/53/531b4e444c034af7af470f6c26faba70cab4c92057b2959087676c9720c6289d.jpg Pretty sure this is relevant one way or another. + honcho and TruHart1 2 Link to comment Share on other sites More sharing options...
+ Gar1eth Posted March 7, 2016 Share Posted March 7, 2016 Source That's a good one. But I thought this was the world's funniest joke: Two hunters are out in the woods when one of them collapses. He doesn't seem to be breathing and his eyes are glazed. The other guy whips out his phone and calls the emergency services. He gasps, "My friend is dead! What can I do?" The operator says, "Calm down. I can help. First, let's make sure he's dead." There is a silence; then a gun shot is heard. Back on the phone, the guy says, "OK, now what?" Gman + WmClarke and + Oliver 2 Link to comment Share on other sites More sharing options...
+ Gar1eth Posted March 7, 2016 Share Posted March 7, 2016 http://cdn.shopify.com/s/files/1/0183/8017/products/DSC_0022.jpg?v=1456527389 And my own. Gman AdamSmith, + WmClarke, + Oliver and 1 other 4 Link to comment Share on other sites More sharing options...
+ Truereview Posted March 7, 2016 Share Posted March 7, 2016 Talking about grammar... http://media-cache-ec0.pinimg.com/736x/36/58/8f/36588f57d1d53a0261c866c80ef41c50.jpg + WmClarke, AdamSmith, + quoththeraven and 4 others 7 Link to comment Share on other sites More sharing options...
AdamSmith Posted March 7, 2016 Share Posted March 7, 2016 Realtor to southern belle: "Madam, this house doesn't have a flaw." Belle: "Then what do y'all walk on?" TruHart1, + quoththeraven, Zman and 3 others 6 Link to comment Share on other sites More sharing options...
+ glennnn Posted March 7, 2016 Share Posted March 7, 2016 A man traveling calls home to his brother to check on the welfare of his cat. He asks, "How is Tiger?" His brother replies, "He's dead." The man screams, "Oh my God! You can't break it to me like that! That's awful. You have to give me time to adjust and get ready. First, you say, 'He's on the roof and we can't get him down.' Then, when I call the next day, you say that he hasn't eaten and he's looking weak. And then, about the third day, you can tell me he's dead! " "By the way, how is Mom?", he asks. Pause "She's on the roof and we can't get her down." Zman, craigville beach, + Truereview and 5 others 8 Link to comment Share on other sites More sharing options...
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