Understanding of progressive symbols

The introduction of advanced mathematics and algorithms have encountered this thing, talk about their own understanding of it

O,ω,θ,ω and ο

I think it's a comparison of the growth magnitude-size relationship between functions.

The main factors that affect the relationship between the two functions are the coefficients of the highest items and the intrinsic growth properties of the function itself (power level, what function, etc.)

Θ depicts two functions that have the same intrinsic growth properties, so their size is only affected by the constant number of times.

Ω: Non-Progressive, f (n) =ω (g (n)), meaning that f (n) is actually different from the intrinsic growth property of G (n) (because for any constant C, in infinity, there is always f (n) greater than g (n))

ο: Analysis Ibid.

Ω: Probably just because of the constant coefficient, it may be different from the intrinsic growth level

O: Analysis Ibid.

The nature of these evolutionary relationships (the nature of the discussion, then certainly is universal, not because the individual functions have a certain nature in a certain evolutionary relationship, it is said that this property is different for all functions)

The Θ,ω,o is reflexive, and W and O are not necessarily reflexive.

Five evolutionary relationships are transitive

Θ is symmetrical, and the other four types are not.

There is a transpose symmetry between Ω and O

Finally, there are infinitely many functions (or the characteristics of the functions are different, ever-changing), not all functions have a gradual relationship, the asymptotic relationship is simply from the growth of the relationship between the characterization of the two functions, any method of research function relationship can not always work.

The evolutionary relationship is valuable in studying the operational cost of an algorithm on a large scale.

Understanding of progressive symbols