# This is wrong, but I don't remember why. **URL:** \ **Category:** Factual Questions\ **Created:** [November 10, 2000, 6:44pm UTC](https://boards.straightdope.com/t/this-is-wrong-but-i-dont-remember-why/40679 "2000-11-10T18:44:43Z")\ **Posts on this page:** 5\ **Page:** 1
**Author:** ![lovelee](https://avatars.discourse-cdn.com/v4/letter/l/439d5e/32.png) [@lovelee](https://boards.straightdope.com/u/lovelee)\ **Post date:** [November 10, 2000, 6:44pm UTC](https://boards.straightdope.com/t/this-is-wrong-but-i-dont-remember-why/40679/1 "2000-11-10T18:44:43Z")
This is wrong, but I’m not sure where the logic fault lies. Can someone more mathematically inclined point it out? Given: a = b ``` Then: ab = a^2 ab - b^2 = a^2 - b^2 b(a - b) = (a + b)(a - b) b = a + b b = 2b 1 = 2 ``` ---
**Author:** ![CalMeacham](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/calmeacham/32/35_2.png) [@CalMeacham](https://boards.straightdope.com/u/CalMeacham)\ **Post date:** [November 10, 2000, 6:53pm UTC](https://boards.straightdope.com/t/this-is-wrong-but-i-dont-remember-why/40679/2 "2000-11-10T18:53:04Z")
Since you start with the assumption that a = b, you have that a-b = 0. When you divide both sides by a-b you are dividing by zero, which is a no-no. Looked at another way, before you divide by a-b the two sides are equal because each side is something multiplued by zero, which is itself zero, so both sides are equal regardless of what the something is (unless the something is infinity, but it isn’t in your example). 1 X 0 = 2 X 0, so there’s no contradiction ---
**Author:** ![pepperlandgirl](https://avatars.discourse-cdn.com/v4/letter/p/f17d59/32.png) [@pepperlandgirl](https://boards.straightdope.com/u/pepperlandgirl)\ **Post date:** [November 10, 2000, 6:58pm UTC](https://boards.straightdope.com/t/this-is-wrong-but-i-dont-remember-why/40679/3 "2000-11-10T18:58:58Z")
Alright, let’s just substitute “2” in for all the unknowns **Given: a = b** –\>2=2 **Then: ab = a^2** —\> 4=4 **ab - b^2 = a^2 - b^2** —\> 2(2)-4=4-4–\>0 **b(a - b) = (a + b)(a - b)** —\>2(2-2)=(2+2(2-2) 2(0)=(4)(0) 0=0 **b = a + b** ----\> 2=4----\> Unless things have changed since I took Algebra I, 2 does not equal 4 **b = 2b —\>** 2=4—\> 2 still does not equal 4 **1 = 2** —\> No more than 2 equals\*\*\* \*\*\*\*disclaimer: I’m NOT a math person, and I probably screwed this up horribly. Please do not laugh at me too much. ---
**Author:** ![lovelee](https://avatars.discourse-cdn.com/v4/letter/l/439d5e/32.png) [@lovelee](https://boards.straightdope.com/u/lovelee)\ **Post date:** [November 10, 2000, 7:10pm UTC](https://boards.straightdope.com/t/this-is-wrong-but-i-dont-remember-why/40679/4 "2000-11-10T19:10:18Z")
Sneaky, sticking that division by zero in there. Everything looks correct, so you tend to not plug in real numbers… which is, of course, what would lead you to realize what they were having you do. Thanks! ---
**Author:** ![wring](https://avatars.discourse-cdn.com/v4/letter/w/838e76/32.png) [@wring](https://boards.straightdope.com/u/wring)\ **Post date:** [November 10, 2000, 7:22pm UTC](https://boards.straightdope.com/t/this-is-wrong-but-i-dont-remember-why/40679/5 "2000-11-10T19:22:10Z")
well, that was exciting. I’ve been out of school since 1972. I wasn’t a math major, but I did tutor a whole lot of folks in algebra etc. back then (my buddy Paul owes me BIG time for passing algebra). And, I figured it out, too… I’ll have to thank my math teacher.