Non-Real Numbers, Undefined Numbers, and Empty Sets. ... This states that a set of numbers exists theoretically, but can't contain anything. This is for when something can not be done, like dividing by zero, because it is impossible (or very, very hard) to divide something by nothing.

Does undefined mean not a real number?

An expression in mathematics which does not have meaning and so which is not assigned an interpretation. For example, division by zero is undefined in the field of real numbers.

Is undefined the same as not real?

The difference between "undefined" and "does not exist" is subtle and sometimes irrelevant or non-existent. Most textbook definitions of slope of a line say something like: The line through points (x1,y1) and (x2,y2) is the ratio: ... But that also means that the slope of such a line does not exist.