Solved: MONOTONIC () in SQL JOIN - SAS Support Communities
2020年1月31日 · As stated here, MONOTONIC() is an undocumented function and the way it assigns each number to each observation is not stated when it comes to aggregating multiple data sets—" If the MONOTONIC function is used in an SQL procedure that aggregates data then the function may return non-sequential or missing results.
MONOTONIC function in PROC SQL - SAS Communities
2018年7月5日 · The MONOTONIC function is an undocumented SAS function. It needs no input parameters and if any input parameters are provided, these are ignored. The function counts the number of times it is called and returns an ascending sequence of integers, starting at 1. The function can be used in an expressi...
education - Monotonous function or monotonic function
2015年4月12日 · Monotonic describes something this is unchanged or altered, such as the function in maths whereas Monotonous describes something lacking in variety and is usually used in reference to tone. Share Cite
analysis - How can I prove the monotonicity of a function ...
Strictly monotonic function on an ordered set implies injectivity, when is the converse true? Hot Network Questions Who can be a primary supervisor for a PhD student?
What is the point of the term "monotonic" when analyzing …
2015年3月17日 · To me, it seems useless to specify if it is monotonic or not as specifying whether the sequence increase/decrease or not will automatically indicate it. Now my question is, is there something that I misunderstood about monotonic sequences, or specifying it is just useless/was just in the goal of seeing if we properly understand the concept ?
Is $\sin(x)$ a monotonic function? - Mathematics Stack Exchange
2018年10月20日 · (FWIW, often in a casual calculus context one will hear a function which reverses the order everywhere also called a monotonic function or "monotonic decreasing function", but technically a better term from a theoretician's pov is "anti-monotonic" or "antitonic" function, since this is still a change of order.
Monotonicity at a Point - Mathematics Stack Exchange
2018年6月19日 · A good way of putting it is from Wolfram MathWorld: A function is monotonic if its first derivative (which need not be continuous) does not change sign. $\endgroup$ – rb612 Commented Jun 19, 2018 at 6:57
Sum of monotone functions - Mathematics Stack Exchange
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Prove that if a continuous function is injective, then it is monotonic
$\begingroup$ @HagenvonEitzen: I learned a function is monotonic if the preimage of a connected set is connected, so I don't think you need ordering at all, and under this definition, you would have to include either $-3$ or $0$ in your example so that the image is connected.
Every continuous open mapping $\\mathbb{R} \\to \\mathbb{R}
2020年7月13日 · Prove that every continuous open mapping from $\mathbb{R} \to \mathbb{R}$ is monotonic I want to prove it only (or mostly) using arguments and concepts from topology, and not from analysis. I don't have anything that I think is useful or correct yet.