A Proof that 0 = 1 (Can You Spot the Mistake?)


American Today News

Okay, so here’s another little fun problem Since the division problem turned out to be so much fun the multiplication and division one. Here’s another one that Somebody pointed out to me so I think it’s just I don’t know let’s take a look so So negative twenty well That certainly equals negative 20 no arguments there, I think Let’s break up negative 20. I’m gonna break it up on the left I think I’m gonna write that as 16 minus 36 certainly you still get negative 20 there and On the right side. I’m gonna write that as 25 minus 45 okay, so Now I’m gonna rewrite things a little bit more I’m gonna rewrite 16 is 4 squared and then I’m Gonna rewrite 36 as 4 times 9 On the right side. I’m gonna rewrite 25 as just 5 squared and then I’m Gonna rewrite 45 as 5 times 9 and Alright, well, I think what I’m gonna. Do now is I’m Gonna add To both sides and the number that I’m gonna add to both sides is I’m Gonna add 81 over 4 All right, so that’s what we’ve got so far well actually I think we can factor this now a little bit, so we can do a couple things here and You know you can you can check that this all works, so I’m gonna leave the 4 squared alone We can just rewrite 4/9 pretty easily, I’m Gonna write that as 2 Times 4 times 9 over 2 so I’m just breaking up the 4 over 9 here a little bit and then I’m Gonna rewrite 81 over 4 as 9 Over 2 Squared on the right side.

I’m gonna do the same thing. So we’ve got 5 squared What I’m gonna do here is I’m gonna write this as 2 times 5 Times 9 over 2 and then plus 9 over 2 squared Okay, so you know we’re just basically just the Tube and the nine halves would cancel hey give us back our or our nine that We had up there so all right so far so good well the reason why we do.

This is this now factors nicely this actually factors as 4 minus 9 over 2 Times 4 minus 9 over 2 And the right side is gonna factor as 5 5 minus 9 over 2 Times 5 minus 9 over 2 All right, well What that tells us is well. We’ve got 4 minus 9 over 2 squared that equals 5 minus 9 Over 2 Squared and now well that means 4 minus 9 over 2 equals 5 minus 9 over 2 and well, we could add 9 over 2 to both sides so that tells us that 4 equals 5 and well if we subtract 4 from both sides That now tells us that 0 equals 1 so proof complete .

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