# Questions tagged [definitions]

For questions related to the issue of concepts of definitions.

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### Why should or shouldn't we teach functions to 15 year olds?

Background The students in my country are supposed to be able to work with and answer questions about functions at the age of around 15. This is asserted in the standard mathematics curriculum for ...
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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. ...
102 views

### When a geometrical figure a special case of another [closed]

Squares are special types of rectangles. Are circles special types of ellipses/ovals? Are cones special types of pyramids? I guess the answer is no because of the 2D basis: circles are not special ...
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### Why define the names of quadrilaterals so that some categories (rhombus and rectangle) intersect and some (kite and trapezoid) are disjoint?

We're using Pearson's Geometry in my class. As terms are defined there, Parallelograms include Rhombi (congruent sides), Rectangles (right angles), Squares (congruent sides and right angles, i.e. ...
361 views

### Alternative limit for e

I have recently worked with some students motivating the development of $e^t$ and $e^{t i}$ as summing change over time, basically informally solving differential equations. My motivation for this is ...
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### 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 ...
411 views

### Explaining subjects whose justification requires demanding technical content

This is my first question and I hope it's appropriate. Often in the process of teaching a subject I start with examples of a phenomenon, exhibiting similar properties between the examples and ...
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### Differential equations - definitions

I am having a great deal of trouble with the definitions used throughout the book so far - i.e. linear, homogenous, non-homogenous, etc. I am not sure why exactly they are useful to know. I am having ...
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### Against introducing precise definitions first

After introducing eight different ways of viewing the derivative of a function (infinitesimal, symbolic, logical, geometric, rate, approximation, microscopic), Thurston, in his famous essay, ...
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### For purposes of teaching, should constant functions be considered “linear functions”?

I can see arguments both for and against classifying constant functions as linear functions. Against: "Linear function" means "first-degree polynomial function", and constant functions are not first-...
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### In Polynomial Form, After Simplification (But Not Before!)

We know that $\dfrac{(x^2+1)x^3}{x^2+1}=x^3$ and $(\sqrt{|x|})^4=x^2$ for every $x\in \mathbb{R}$. Can $\dfrac{(x^2+1)x^3}{x^2+1}$ and $(\sqrt{|x|})^4$ be called polynomials? Is there a general name ...