Luisitin 12 Posted January 24, 2019 Report Share Posted January 24, 2019 a = b a^2 = ab a^2-b^2 = ab-b^2 (a+b)(a-b) = b(a-b) a+b = b a = b so, 2b = b 2 = 1 Quote Link to post Share on other sites
Gramps 2,227 Posted January 24, 2019 Report Share Posted January 24, 2019 But if a = b, then a - b = 0. Meaning, step 4 would evaluate to (a+b) 0 = b (0), which evaluates to 0 = 0. Step 5 and onwards are invalid because you can't divide by 0. 1 1 Quote Link to post Share on other sites
Conan Edogawa 837 Posted January 25, 2019 Report Share Posted January 25, 2019 (edited) Your proof's a bit cliched. a = b, and so a - b = 0, which means you're dividing by 0, which is not allowed. Edited January 25, 2019 by IntegrationNation 1 Quote Link to post Share on other sites
Candy 804 Posted January 25, 2019 Report Share Posted January 25, 2019 Ah, an old math trick. My teacher in high school showed us this for us to find the flaw. Of course, if a=b, a-b is 0. Like Gramps said, you cannot divide by zero. Therefore, this proof is invalid. 1 Quote Link to post Share on other sites
Conan Edogawa 837 Posted January 25, 2019 Report Share Posted January 25, 2019 This reminds me of another illusory proof.. 0 = 0 + 0 + 0 + 0... = (1 - 1) + (1 - 1) + (1 - 1)... = 1 - 1 + 1 -1 + 1 - 1 +... = 1 + (-1 + 1) + (-1 + 1)... = 1 + 0 + 0... = 1. What's wrong with my proof? 1 1 Quote Link to post Share on other sites
Serpent-Z 84 Posted January 25, 2019 Report Share Posted January 25, 2019 6 hours ago, IntegrationNation said: This reminds me of another illusory proof.. 0 = 0 + 0 + 0 + 0... = (1 - 1) + (1 - 1) + (1 - 1)... = 1 - 1 + 1 -1 + 1 - 1 +... = 1 + (-1 + 1) + (-1 + 1)... = 1 + 0 + 0... = 1. What's wrong with my proof? There's a -1 hiding at the end of the last two steps. 1 Quote Link to post Share on other sites
Shawnic 2,977 Posted January 25, 2019 Report Share Posted January 25, 2019 11 hours ago, IntegrationNation said: This reminds me of another illusory proof.. 0 = 0 + 0 + 0 + 0... = (1 - 1) + (1 - 1) + (1 - 1)... = 1 - 1 + 1 -1 + 1 - 1 +... = 1 + (-1 + 1) + (-1 + 1)... = 1 + 0 + 0... = 1. What's wrong with my proof? You haven't considered all the terms while forming pairs i.e. a -1 is missing in your pairing step. Quote Link to post Share on other sites
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