Do have a look at the DEFINITIONS section of my recent post

https://howardat58.wordpress.com/2018/02/17/the-chain-rule-and-the-theory-2/

]]>I’m glad to know I’m not the only one who struggles with this. And thanks for the comment. Interesting.

]]>There was a comment about the equals sign that I’d like to elaborate on.

The = sign can mean either assignment or equality, and programming languages use different symbols for each (in Python, for example, single = for assignment and double == for equality), because it’s essential to define variables before relating them. For example, if y = 2 and x = y, then x == y, but if x or y hasn’t been defined yet, then asserting that x == y will throw an error. When dealing with functions and equations in mathematical notation, the = usage tends to be less precise, because nothing will crash (except perhaps the students’ minds). But it’s often helpful to distinguish = and == in mathematical notation as well, because it clarifies the underlying logic and assumptions. For example, if h(c) = c + 15 and p(c) = c + 3 (function definitions), then h(c) + p(c) == 2c + 18 (a statement of equality based on the definitions, NOT an assignment).

That seems to be contradiction

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