In Baby Rudin a subset E of a metric space X is defined to be connected if "E is not a union of two nonempty separated sets."
This may be nit picking, but should this not be
E is not a union of two or more seperated sets
?
Wikipedia agrees. To be super nit picking, by Rudin's definition (and taking it super literally) a set that is the union of three nonempty separated sets would be connected since... two is not equal to three.
A positive number is defined as being greater than $0$. If $x>1$, then can we say that $x$ is not positive since $1$ is not equal to $0$?
A set that is the union of three separated sets is also a union of two separated sets.