InfinityInfinity sometimes appears as the result of a calculation:
Precision[1]
But Infinity it often used as a value in expressions:
1 / Infinity
Infinity + 100
Infinity often appears in sum and limit calculations:
Sum[1/x^2, {x, 1, Infinity}]
Limit[1/x, x->0]
However, Infinity a shorthand for DirectedInfinity[1]:
FullForm[Infinity]
See also DirectedInfinity.