**stevens@teklabs.UUCP** (09/12/83)

Two articles proved that -1=1. One by Steve Summit went like -1 = sqrt(1) -1 = 1 I also am not quite sure of what makes this go wrong, but I have observed that the square root of 1 is also -1. The other article said something like sqrt(-1)*sqrt(-1) == -1. This is true, but I think the conflict in both cases could probably have been avoided if it was done in complex numbers. i.e. let 2*pi*i e = 1 etc. etc. -- Steve Silberberg

**dje@5941ux.UUCP** (09/14/83)

There seems to be some confusion over the "1 = sqrt(1) = -1" reasoning. sqrt(...) is a real-valued function that for each non-negative x maps it into the unique non-negative y for which y*y = x. Any equality of the form "sqrt(x) = y" can therefore make sense only if y is non-negative! sqrt(1) = 1, NOT -1. Although we may say (loosely) that -1 is "a" square root of 1, the abuse of language here does not extend to the use of the sqrt(...) function or to any assertion of equality other than (-1)*(-1) = 1. Dave Ellis / Bell Labs, Piscataway NJ ...!{hocda,ihnp4}!houxm!houxf!5941ux!dje ...!floyd!vax135!ariel!houti!hogpc!houxm!houxf!5941ux!dje