The discussion centers on the identity function and its properties, specifically focusing on strictly increasing functions. It is established that if a function f(x) preserves ordering such that if x < y then f(x) < f(y), it does not necessarily imply that f(x) is the identity function. The example of f(x) = 2x is presented to illustrate that strictly increasing functions can also satisfy the ordering condition. Therefore, the identity function is just one of many functions that can meet these criteria.
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It does not necessarily follow that f is the identify function. Any strictly increasing function satisfies the given conditions, not just f(x) = x.Gabbey said:Let's say I have a function that preservers ordering i.e if x<y then f(x)<f(y) for all x. Obviously it must follow that it's the identity function but how can I approach this?