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pivoxa15
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This operator, captial O is used in physics such as electrodynamics and can be placed in front of functions (i.e. Of(x)). Could somone explain it clearly with a definition. In what situations is it used?
0rthodontist said:Asymptotic notation has to do with "within a constant multiple" rather than just strictly greater than or less than. You write
f(n) = O(g(n)) iff there is some N and some k > 0, where for any n >= N, you have 0 <= k * f(n) <= g(n)
0rthodontist said:One book I have uses f(n) [tex]\in[/tex] O(g(n)) instead of f(n) = O(g(n)) to emphasize that O(g(n)) actually is a set of functions that are asymptotically within a constant multiple of each other.
pivoxa15 said:It seems the order (O) of f(x), which is g(x) (or f(x)=O(g(x))) provides the largest order of magnitude of growth for f(x).
shmoe said:It's not the largest order of magnitude of growth, rather an upper bound for the order of the growth. It doesn't need to be optimal in any way, x^2=O(x^34), this is as x->infinity.
pivoxa15 said:With your example, there is no doubt it is correct but o can be used as well and is a better alternative. Because all o can be replaced by O (but not vice versa) so it means it is always best to use o if possible (otherwise what is the point of having o).
There is no doubt O is used more often than o and that could be why Wiki only has one entry called big O, not small o.
Operator O in Physics refers to the mathematical representation of an observable quantity, such as position, momentum, or energy. It is used to describe the state of a physical system and its evolution over time.
Operators are used in quantum mechanics to represent physical observables and their corresponding equations of motion. They are applied to wave functions to obtain information about the state of a system and its behavior.
Some common examples of Operator O in Physics include the position operator, momentum operator, and energy operator. These operators are represented by mathematical symbols and are used in various equations and calculations in quantum mechanics.
Operator O in Physics differs from other mathematical operators in that it is specifically used to represent physical observables and their associated equations of motion. It takes into account the principles of quantum mechanics and is not limited to classical mechanics.
The use of Operator O in Physics has greatly impacted our understanding of the physical world, particularly at the quantum level. It allows us to make predictions and calculations about the behavior of particles and systems, and has led to groundbreaking discoveries and technologies.