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Dragonfall
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Is there an easy description for all the real to real functions that are order-preserving? I can only think of linear functions
What do you mean by "order-preserving?" Is it the idea that if a < b, then f(a) < f(b)? If so any function that is strictly increasing satisfies the latter inequality. If you mean something different, you need to clarify your question.Dragonfall said:Is there an easy description for all the real to real functions that are order-preserving? I can only think of linear functions
mfb said:Uniformly random where?
Every f is "decomposable" that way, simply set f_1(x)=f(x), f_2(x)=x (or vice versa).
Knowing only one of an arbitrary and unknown "decomposition" makes the task impossible - see my example, one of the functions could be just the identify function.
I think it would really help if you give more context. What do you actually want to do?
So who is supposed to know what? What is the protocol you want to use, and what is the result?Dragonfall said:I'm trying to come up with something similar for two ordered committed numbers.
A general order-preserving function is a mathematical function that preserves the order of elements in a set. This means that if two elements in the input set are in a certain order, the resulting output set will also have those elements in the same order.
A general order-preserving function differs from a regular function in that it specifically focuses on preserving the order of elements. Regular functions may not necessarily maintain the order of elements in the input set when producing the output set.
Some examples of general order-preserving functions include sorting algorithms like bubble sort, selection sort, and insertion sort. These algorithms rearrange elements in a set while preserving their original order.
Preserving order is important in mathematics because it allows us to accurately compare and analyze sets of data. By maintaining the order of elements, we can make meaningful conclusions about the relationships between different elements in a set.
No, not all order-preserving functions are considered general order-preserving functions. A general order-preserving function must preserve the order of elements in all possible inputs, while other order-preserving functions may only preserve order in certain cases or for specific types of inputs.