OK so In calculus Extended real line?
Formal operations:
A formal calculation is one carried out using rules of arithmetic, without consideration of whether the result of the calculation is well-defined. Thus, it is sometimes useful to think of a/0, where a 0, as being \infinity. This infinity can be either positive, negative, or unsigned, depending on context.
Real projective line:
The set {R} U \infinity is the real projective line, which is a one-point compactification of the real line. Here \infinity means an unsigned infinity, an infinite quantity that is neither positive nor negative. This quantity satisfies -\infinity = \infinity, which is necessary in this context. In this structure, a/0 = \infinity can be defined for nonzero a, and a/\infinity = 0. It is the natural way to view the range of the tangent and cotangent functions of trigonometry: tan(x) approaches the single point at infinity as x approaches either +\pi/2 or -\pi/2 from either direction.
This definition leads to many interesting results. However, the resulting algebraic structure is not a field, and should not be expected to behave like one. For example, \infinity + \infinity is undefined in the projective line.
Riemann sphere, which is of major importance in complex analysis. Here too \infinity is an unsigned infinity – or, as it is often called in this context, the point at infinity. This set is analogous to the real projective line, except that it is based on the field of complex numbers. In the Riemann sphere, 1/0=\infinity, but 0/0 is undefined, as is 0\times\infinity.
Extended non-negative real number line:
The negative real numbers can be discarded, and infinity introduced, leading to the set [0, infinity], where division by zero can be naturally defined as a/0 = infinity for positive a. While this makes division defined in more cases than usual, subtraction is instead left undefined in many cases, because there are no negative numbers.
Still you are mixing maths but I get it...