41
votes
Accepted
Is there a canonical name for a polynomial-like expression allowing for negative powers?
There is also the term "Laurent series", where we allow an infinite number of terms...
$$
\dots +5x^{-3} + 2x^{-2} + 3x^{-1} + 2 + 4x - 7x^2+\dots
$$
So perhaps yours is a "finite ...
- 7,205
24
votes
Accepted
How can I validate the existence of percentages above 100?
The formula to express a value $X$ as a percentage of another value $Y$ is simply $Percentage= (X/Y)×100$. It is simply a ratio of numbers (a multiplicative factor), times 100. There is absolutely ...
- 879
17
votes
Is there a canonical name for a polynomial-like expression allowing for negative powers?
You can call it a "polynomial in $x$ and $x^{-1}$" or a "polynomial function of $x$ and $x^{-1}$". The idea is that you are taking a two variable polynomial $p(x,y)$ and then ...
- 23.2k
11
votes
How can I validate the existence of percentages above 100?
From a practical standpoint, the horse has long been out of the barn on quoting price increases and other measures of growth as percentages (furthermore, one will hear static ratios being quoted as ...
- 1,054
10
votes
Accepted
what could be some replacement language for the term "spoon feeding"
No one can make any universal guarantees as to whether or not any particular student may find your usage of spoon-feeding or any other term offensive or insensitive. However, spoon-feeding as a ...
- 1,054
9
votes
How can I validate the existence of percentages above 100?
Let me digress into material probably for HSM Stack Exhcange: Arithmetic and math in general is an abstraction to our real world counting and measuring (from which mathematics originated from).
The ...
- 209
7
votes
How can I validate the existence of percentages above 100?
The way I like to put it is: ‘Per cent’ means nothing on its own. Only ‘per cent OF …’ is meaningful.
A percentage is simply another way of writing a ratio (like a vulgar fraction, or a decimal ...
- 305
7
votes
Accepted
What is the terminology for integers with the same oddness or evenness?
Expanding on a comment by @TomKern: The word you're looking for is parity.
You can see it in most standard English dictionaries, such as Merriam-Webster, here:
4 a: the property of an integer with ...
- 22.8k
7
votes
‘Induction on’ vs ‘Induction with respect to’ in math
Yes, these expressions mean exactly the same thing. Both are correct; in my experience, ``induction on n'' is more common. Usually, the shorter the phrase, the more likely it is to be widely adopted....
- 181
6
votes
How can I validate the existence of percentages above 100?
If a student in my class believed this, I would respond as follows:
I would draw two pizzas in boxes. If someone eats the contents of one box, they ate one pizza and one pizza is left over. If ...
- 7,839
6
votes
Is coefficient same as constant?
I'd say that the video is not using the best word. I would call that constant the coefficient.
Constant means that it is a number and not a variable. That's true. But the word coefficient conveys more ...
- 19.2k
6
votes
Is there a canonical name for a polynomial-like expression allowing for negative powers?
In comments, Eike Schulte and paul garrett mentioned that the standard term seems to be "Laurent polynomials."
Gerald Edgar's answer also mentions this term in passing, but I figured that it ...
6
votes
What should I call the "important" values of x?
When graphing a function (or just investigating it from some point of view), it is, indeed, useful to look at some special points where the behavior changes in some way. Most of them have well-...
- 3,044
6
votes
Accepted
Triples or triplets in Pythagoras theorem
The word “triple” is appropriate here because $(3,4,5)$ is a tuple consisting of three elements.
In mathematics, a tuple is a finite ordered list (sequence) of elements... Mathematicians usually ...
- 1,809
6
votes
Importance of etymological approach to terminology
I think etymology is not useful in the way proposed by the OP.
But here is a case in mathematics where etymology can help with spelling:
parallelepiped
The etymological analysis is: parallel + epi + ...
- 7,205
5
votes
Is there a canonical name for a polynomial-like expression allowing for negative powers?
The question is about what to call these expressions/functions when teaching the first basic properties of derivatives. All of the names proposed in previous answers would just make this harder for ...
- 19.2k
5
votes
How can I validate the existence of percentages above 100?
Obviously the instructor's comments were total nonsense. The OP put forward a clear argument that showed he was wrong, he got unjustifiably defensive, and wound up doubling-down on his rhetoric, ...
- 22.8k
5
votes
Accepted
What should I call the "important" values of x?
For function transformations I use "base point" ($y=a^x$ has base point $(0,1)$, $y = \frac{1}{x}$ has base point $(0,0)$, even though it isn't on the graph).
In calculus I use "point ...
- 3,858
4
votes
How can I validate the existence of percentages above 100?
Doesn't this come down to whether you are looking at parts of a single thing, or comparing parts of two things?
If you are looking at the parts of a single thing, like "How full is the gas tank?&...
4
votes
How can I validate the existence of percentages above 100?
This math educator’s argument seems to be grounded in language more than in mathematics. It should be self-evident that the mathematical processes of percentages are useful for things like price ...
- 364
4
votes
Is there a canonical name for a polynomial-like expression allowing for negative powers?
I would also like to suggest posynomials $$f(x_1,\cdots,x_n)=\sum_{k=1}^Kc_kx_1^{a_{1,k}}\cdots x_n^{a_{n,k}}.$$ These generalise the idea to a multivariate setting with interaction terms, and the ...
4
votes
what could be some replacement language for the term "spoon feeding"
A term for the same or similar that has positive connotations is 'scaffolding'.
I want my students to understand the connection between a function's graph and the graph of its derivative, so I ...
- 19.2k
4
votes
What should I call the "important" values of x?
I've used the term "reference point" or "reference coordinate" when referring to the points on the original function, compared to their transformed locations. I've expected my ...
- 3,947
3
votes
Why do we explicitly state the equality of two things when we know they're equal
If I write
$$
202384569+4765923845-141243678 =
$$
then go off and think a bit, do a hand calculation, or consult a calculating device, and come back and complete it to
$$
202384569+4765923845-...
- 1,038
3
votes
Word for an object being extended: Given F, a function that extends F is called an extension and F is called the extension __?
I'd just say "the original function", having a pretty good colloquial sense, rather than create a technical word. Yes, if you are considering such stuff in a more extravagant way (e.g., in a ...
- 13.8k
3
votes
Why do we explicitly state the equality of two things when we know they're equal
Your answer is good for showing that indeed we sometimes arrive at an equality via an experimental approach: We try to relate different quantities we observe in day to day life to each other and ...
- 329
3
votes
How can I validate the existence of percentages above 100?
You can't use 110% of the gas tank.
He drilled into his students that 100% was the literal maximum.
This reminds me of my earlier comment that any discussion of "too much" or "too ...
- 1,692
3
votes
How can I validate the existence of percentages above 100?
Percent almost literally means "a hundredth". It's a way of expressing fractions. 150% is a factor of 1.5, etc. Now, what use one makes of these factors is besides the point.
The usual ...
3
votes
Why is there variation in the meaning of "Standard form" for a quadratic?
When considering transformations of the "basic" $y=x^2$, there is not much else you can do besides
Vertical shift
Horizontal shift
Scaling
The first is achieved by adding a constant to $...
- 240
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