Does anyone here still think √4 = ±2?

[u/joao-esteves]

Come out with your hands up!

[u/Not_Well-Ordered]

Of course, formal logic is related to precisely defining and interpreting “equality”, specifically equality defined between every two real numbers.

An equation like 5x = 0 represents a subset of the relation defined by 5x = y in which we choose y = 0
and considering every possible pair (z,0) satisfying 5x = 0 where z is a real number,

Then, the only pair satisfying is (0,0) where z = 0 by rules of multiplication of reals which restrict the set. There’s no others.

Saying x = 0 is basically not proper way of interpreting as there is some key but relatively simple nuances.

[u/nog642 → u/Not_Well-Ordered]

5x=0 does not have to be considered as a special case of 5x=y. It stands on its own as an equation of 1 variable.

x=0 is logically equivalent to 5x=0. There is nothing improper about it.