Editing Asymptotic analysis (section)

== Properties ==
If <math>f \sim g</math> and <math>a \sim b</math>, then, under some mild conditions,{{Explain|reason=Many readers might like to know what the exact conditions are.|date=July 2021}} the following hold:

* <math>f^r \sim g^r</math>, for every real {{mvar|r}}
* <math>\log(f) \sim \log(g)</math> if <math>\lim g \neq 1 </math>
* <math>f\times a \sim g\times b</math>
* <math>f / a \sim g / b</math>

Such properties allow asymptotically equivalent functions to be freely exchanged in many algebraic expressions.

Also, if we further have <math>g \sim h</math>, then, because the asymptote is a [[transitive relation]], then we also have <math>f \sim h</math>.