As of May 31, 2023, we have updated our Code of Conduct.

# Tag Info

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 ...
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 ...

### 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 ...

### 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 ...
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### 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 ...

### 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 ...

### 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 ...
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### 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 ...

### ‘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....

### 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 ...

### 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 ...

### 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 ...

### 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-...
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### 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 ...

### 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 + ...

### 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 ...

### 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, ...
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 ...

### 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?&...

### 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 ...

### 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 ...

### 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 ...

### 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 ...

### 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-...

### 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 ...

### 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 ...

### 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 ...
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 \$...