What are the properties of infinity and infinitesimal?

What are the properties of infinity and infinitesimal?

The definition of infinitesimal: the variable whose limit is zero is called infinitesimal
(1) Infinitesimal is a variable and cannot be confused with very small numbers;
(2) Zero is the only number that can be infinitesimal
The definition of Infinity: the variable whose absolute value increases infinitely is called infinity
(1) Infinity is a variable and cannot be confused with large numbers;
(2) Infinity is a special unbounded variable, but unbounded variable may not be infinite
(3) The algebraic sum (product) of infinitesimals may not be infinitesimal;
Theorem in the same process, the reciprocal of infinity is infinitesimal; the reciprocal of infinitesimal which is not zero is infinity
one
-= Lim X - > 0 (x > 0) in Y, then y - > is positive infinity at this time
x
same
one
-In = - y, Lim X - > 0 (x > 0), then y - > negative infinity
x