I am wondering if there is any difference between non-positive and negative numbers?
I think that negative numbers mean "negative real numbers"
and "Non-positive numbers" are negative real numbers and complex numbers.
Is it right?
Since there is no way to tell complex numbers are negative or positive.
So when It says non-positive, I think complex numbers are included.
Best Answer
"Positive numbers", "Negative numbers", "Nonpositive" and "Nonnegative" only make sense when talking about the real numbers (or some other field with a positive and negative decomposition). It does not work in the context of complex numbers.
Positive (real) numbers: $\mathbb{R}^+ = (0,\infty)$
Negative (real) numbers: $\mathbb{R}^- = (-\infty, 0)$
Non-positive (real) numbers: $\mathbb{R}^-\cup\{0\} = (-\infty,0]$
Non-negative (real) numbers: $\mathbb{R}^+\cup\{0\} = [0,\infty)$
That is to say, the difference between positive and non-negative numbers is that for positive numbers it does not include zero, whereas for non-negative it does include zero.
When no distinction is made, it is assumed that the person means real numbers.