Algebra - Proof that -1 = 1 and 1 = 3

383

Soumyabrata Mondal ·2013-03-05 00:36:46

for 2nd one (2) step

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Soumyabrata Mondal log(-1) is not possible
Upvote·0· Reply ·2013-03-05 00:41:56
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Shaswata Roy ·2013-03-05 00:53:43

@Soumyabrata Mondal
Even I had thought of that before.
But you see,
\dpi{200} \fn_cs e^{i\pi} = -1\Rightarrow log(-1) = i\pi
Hence log(-1) does have a value.

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Soumyabrata Mondal i(pi) is nt real. i is an imaginary number.
Upvote·0· Reply ·2013-03-05 04:07:58
Shaswata Roy Doesn't matter if it is not real...as long as it is some value which can be cancelled from both the sides.
Upvote·0· Reply ·2013-03-05 04:22:58
Shaswata Roy Actually I had seen this on a post given by a Singaporean olympiad trainer.He said that log of a negative no. can be taken.
Upvote·0· Reply ·2013-03-05 04:24:22
Shaswata Roy All I know is that the answer has got something to do with the property of log (or antilog don't know,:P) and it has got something to do with one to one correspondence or something like that.
Upvote·0· Reply ·2013-03-05 04:26:20
Soumyabrata Mondal ok, then I think it is out of my knowledge :-(
Upvote·0· Reply ·2013-03-05 09:47:45
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229

Dwijaraj Paul Chowdhury ·2013-03-05 05:38:21

For 1st one.....
The first question was given in ISI
you cant express two negative nos which are in square root
form as two different roots...i meanâˆš(-1*-1) cannot be written as root-1 *root -1...nd @Roy the question is --"Proof that"?? :-|

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Shaswata Roy Obviously "proof that" cos I am not asking anyone 2 prove anything.It's a "proof" that -1=1 and 1=3.
Upvote·0· Reply ·2013-03-05 05:57:20
Shaswata Roy By the way,thanks for finding out the flaw.
Upvote·0· Reply ·2013-03-05 05:58:01
Dwijaraj Paul Chowdhury ;-)
Upvote·0· Reply ·2013-03-05 08:12:33
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36

Karan Bhuwalka ·2013-03-06 05:16:31

âˆš (-1).(-1) equals 1

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Shaswata Roy Not necessarily....it can be -1 too.
Upvote·0· Reply ·2013-03-06 09:20:37
Soumyabrata Mondal how??
Upvote·0· Reply ·2013-03-06 10:06:04
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Manish Shankar ·2013-03-11 00:03:36

√a/b=√a/√b for positive values of a and b only

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Dwijaraj Paul Chowdhury ·2013-03-12 07:29:02

for the 1st proof
Dekh log er value replace korle
3i*pi=1i*pi
Now LHS=(0,3*pi)
And RHS=(0,pi) by multiplication of complex nos. But as they don't represent the same complex nos. on an argand plane, they cannot be equal. :. Contradiction. LHS is not equal to RHS.

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Shaswata Roy Thanks for stating the obvious :P....It's known that LHS is not equal 2 RHS . I am asking why they are not equal (i.e. what mistake had I made while taking the log).As I had said b4 2 Soumyabrata, it has got something 2 do with one to one correspondence property of log or something like that(don't know).
Upvote·0· Reply ·2013-03-12 07:47:36
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337

Sayan Sinha ·2013-03-12 23:53:12

I think, for the 2nd one,

log is not possible for a negative number.

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Proof that -1 = 1 and 1 = 3

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