2*2=4, 2+2=4, what other number can do that?

if A^2 = B

and A + A = B

Then A^2 = 2A

Or A^2 -2A = 0

A = 0

And

A = 2

The only other answer is zero

This has got to be the most complete and definitive thread ever!

JM

zero is not another valid answer since the question states greater than zero

"what other number can do that?"

None in the domain of integers (except zero).

None in the domain of rational numbers (except zero).

None in the domain of complex numbers (except zero).

None in the domain of octol, hexadecimal or binary numbers, but there are plenty numbers in any space (group) that is onto but not 1 to 1 (i.e. not a isomorphic field).

Example - the number set represented by all positive integers mod any power of 2 might be good candidates (e.g. {X: x element of R, set defined by x mod 16 }, as a trivial example 16 plus 16 = 16 * 16 as there are both zeros of this set. But 8 isn't a zero yet 8 * 8 = 8 + 8 = 0 as 8 + 8 mod 16 = 0 and 8 * 8 mod 16 = 0.

So there are infinite correct answers once you move from fields to groups defined by the mod of any even number (actually any non prime number, given a mod by a prime base is isomorphic hence is a field).

Wow that went so far over my head. Is that like bases g_day?

Yes, a bit - its first year Uni number theory.

None in any domain, where

ab = 0 implies either a = 0 or b = 0

for any a, b in the domain.

Re: 2*2=4, 2+2=4, what other number can do that?


The answer is right there in front of your face. Fractions are allowed. Any fraction that equals 2; 4/2, 6/3, 8/4, 160/80, 345656/172828, etc, etc.

I wouldn't consider 4/2 as different from 2.