# Questions tagged [definitions]

For questions related to the issue of concepts of definitions.

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### In what curricula are “rectangles” defined so as to exclude squares?

Most contemporary curricula define the word "rectangle" inclusively, so that all squares are automatically rectangles. Are there curricula in which this convention is not followed? That is,...
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### How can I motivate the formal definition of continuity?

In order to teach continuity of real valued functions $f:D\to\mathbb R$ one may start with the (in some sense wrong) intuition $f$ is continuous when its graph can be drawn without lifting the pen. ...
2k views

### The definition of natural log and e

I'm asking this question from the point of view of an introductory non-rigorous calculus instructor. Calculus textbooks have different approaches about how to define $e$ and $\ln$. For example, my ...
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### What is a variable?

There are two kinds of answers I'm looking for: What do students think a variable is? What do YOU, the teacher, think a variable is? I'm also interested in why you think a variable is what you think ...
1k views

As mentioned in this question students sometimes struggle with the fact that continuity is only defined at points of the function's domain. For example the function $f:\mathbb R\setminus\{0\} \to \... 2answers 166 views ### Does solving crosswords help with recall of definitions? I have an idea to help with self-study and recall of definitions. It is to create a crossword where the clues are the definitions and the words to solve are the concepts being defined. I haven't ... 9answers 2k views ### Why do students have problems with showing that something is well-defined? How can this be improved? I see a lot of students struggling when they have to show that something is well-defined. I have the feeling that this is often not understood. Two examples: When defining a sequence$x_n= g(x_{n-1}...
Students sometimes ask whether the $x$ in the expression $$2x$$ the same kind of thing as the $x$ in the equation $$2x = 4.$$ In the expression $2x, \;x$ can be any real value. However, in the ...