## Aadarsh 3 years ago Question Of The Day.

Prove that 1 = 2 , 0 = 1 and 1 = 2. I need clever answers.

not this one again D: algbebraic expressions is my final answer

algebraic*

All are requested to try. This is a puzzle question.

5. dpaInc

O + 4 = 5. solve for ooh.

6. Callisto

x = 2x Cross out x -> 1=2 :S

7. lgbasallote

Let a= b Then a^2 = ab a^2 + a^2 = a^2 + ab 2a^2 = a^2 + ab 2a^2 - 2ab = a^2 + ab - 2ab 2a^2 - 2ab = a^2 - ab 2(a^2 - ab) = a^2 - ab --------- ------- a^2 - ab a^2 - ab 2 = 1

U can answer in so many ways. Try all.

whoa...I'm keeping my bf

10. Mathisnotfun

x + x = 4x x(1+1) = 4x (1 + 1) = 4 2 = 4 1 = 2

@lgbasallote answer is thrilling. I was searching for ur answer, LGBA!!!!! Now proceed and u can solve that 1=0 and also 0 = 2.

12. lgbasallote

it's actually a fallacy lol =)) dividing 0 by 0 is illegal :p

13. FoolForMath

@Aadarsh: This is not a puzzle, this is wrong mathematics. Finding the error would be some fun though.

Everything is possible in maths, lgba.

15. dpaInc

dividing by 0 is a fantasy?

Its fun time guys and girls. Lets enjoy

stuff just got real.

18. gurvinder

aad plzz aye koi question hai ..........

19. Callisto

@ffm true, we cannot cancel the variables like that :P

20. apoorvk

let x=0 then 20x = 100x or x = 5x or 1 = 5 :P :p Okayy... proving is one thing. I ll ask you guys this: wherein here is the trouble. Which step did we make the mistake at, so we get such erratic answers that would cause Newton to suffer a heart attack if he ever saw this? ;)

22. apoorvk

oh yeah @foolformath already asked this. so where is the error, aadarsh can you think? (this question was presented in Bansal classes entrance test multiple times)

23. lgbasallote

@Callisto how do you tag @FoolForMath with ffm???

24. apoorvk

like this @ffm

26. apoorvk

:D sorry for the troubles FFM

27. lgbasallote

i dont think @ffm is the same as @FoolForMath yes?

28. FoolForMath

I am not notified with @ffm

29. apoorvk

may be, aadarsh. or the other way around. someone always copies from somebody

@Mani_Jha , @AravindG , @payalvsangle , @heena , @sheena101 , @gurvinder , @Ishaan94 , please try. I have to present this before my seniors and get cash prize.

31. Callisto

Hmmm... I was trying to show that I was responding his words, so .... it doesn't matter if I have really tagged him :P

32. apoorvk

So, Aadarsh where is the trouble. try guessing!

@apoorvk bhai, there is no mistake. Mistake der in assumption.

34. lgbasallote

the fallacy works well

35. Mani_Jha

@As a general rule, you shouldn't multiply or divide an equation by zero.

36. FoolForMath

let x=0 then 20x = 100x or x = 5x or 1 = 5 (How are you cancelling x? This is division by zero)

37. Mani_Jha

(1−2)^2=(2−1)^2=1 1−2=2−1 2=4 1=2 Find out the mistake in this.

Mistake is in this: 1-2 = 2-1

39. KingGeorge

How about a proof that shows $$e=1$$? $\Large e=e^{2\pi i \over 2\pi i}=(e^{2\pi i})^{1 \over 2 \pi i}=1^{1 \over 2 \pi i}=1$

Hats off to @KingGeorge .

41. Mani_Jha

Haha. Good. I used a fallacy to prove another fallacy!

@King , @shruti , @neha2050 , @salini Please try.

43. FoolForMath

$$a^2 = b^2 \implies \pm a= \pm b$$ So there are two solutions.

44. Mani_Jha

@KingGeorge, finding the value of anything to a complex power doesn't make sense. You can't be sure that: $1^{1/2\pi i}=1$

45. KingGeorge

An alternative proof I found online: Let $$2e=f$$. Then $$2^{2 \pi i}e^{2 \pi i} =f^{2\pi i}$$. Since $$e^{2\pi i}=1$$, we know that $$2^{2\pi i}=f^{2\pi i}$$. This means that $$2=f$$. From that we substitute $$f$$ back in, and get $2e=2$Thus, $$e=1$$

46. FoolForMath

@KingGeorge: When a number is raised to a complex power, the result is not precisely defined.

47. FoolForMath
48. KingGeorge

It's the basically the same deal for the second one. $$f^{2\pi i}$$ can get really funky. $$2^{2\pi i}$$ is already funky.

49. apoorvk

exactly. there is a mistake as @ffm just showed. how do you think are you dividing by '0'??

Can we not try to prove that division by zero is indeed possible? At least by this, we can get the Abel Prize.

51. apoorvk

Abel prize. lol

52. apoorvk

you 'll get special academic razzies for that!

Lets hope so!!!!!!!!!!!!!!!!!!!!!!!

54. KingGeorge

@Mani_Jha The actual problem with my original proof is that $\Large e^{{2 \pi i} \over {2 \pi i}} \neq (e^{2 \pi i})^{1 \over {2 \pi i}}$Complex exponents don't do that.

55. Mani_Jha

@Aadarsh, You can't do that. That's why zero is called the 'hero' of Mathematics!

Oooooo! Really??

58. shruti

tumne apne info mei ye sab kya likh dala hai?

Mera naam hai didi!!!!!! Yeh to maine dhamaal se copy kiya hai.!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

60. shruti

cool...yhi kaam kro aur ye kya qestn post kar rakha hai. i felt sumth imp. is there but is'nt

61. PRINCEOFPERSIA

Multiply zero on both sides. 1 x 0 = 2 x 0 0 = 0 1 = 2

63. PRINCEOFPERSIA