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The symbol  has the following values at some finite points  :
The symbol  has the following values at some infinite points  :
The symbol  has the following value at point  :
 is a symbol. It represents an unknown or not exactly determined point (potentially with infinite magnitude) of the complex plane. Often it results from a double limit where two infinitesimal parameters approach zero at different speeds (e.g.  ).
 is a symbol. On the Riemann sphere, it is the north pole approached from exactly east. In the projective complex plane, it is a point at the line at infinity.
 is a symbol. On the Riemann sphere, it is the north pole. In the projective complex plane, it is the line at infinity.
 is a symbol. On the Riemann sphere, it is the north pole together with the direction  how to approach it. In the projective complex plane, it is a point at the line at infinity.
The symbols  ,  ,  , and  have the following complex characteristics:
Derivatives of the symbols  ,  ,  , and  satisfy the following relations:
Simple indefinite integrals of the symbols  ,  , and  have the following representations:
All Fourier integral transforms of the symbols  ,  ,  , and  can be evaluated using the following formal rules:
Laplace direct and inverse integral transforms of the symbols  ,  ,  , and  can be evaluated using the following formal rules:
The symbols  ,  , and  satisfy some obvious inequalities, for example:
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