Memorandum you limit remarkable

o(.)

In pratica the o(.) not fà that to confront 2 functions that are in fractional shape to the aim of being able to replace to one of the 2 one expression in o(.) containing also part of the other function, in such a way can be become simpler. As an example:

x^to= o(1) * to^x

, for x ® 0

In practical between parenthesis there is the term that dominates regarding the other.

for x ® ¥

Arithmetic of the o(.)

o(x^to) o(x^b) = o(x^{min(to , b)})

x³ * o(x^b) = o(x^{b 3})

3 * o(x^b) = o(x^b)

o(x^to) o(x^b) = o(x^{to b})

o(o(x^to)) = o(x^to)