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20 votes
Accepted

Do undergraduates struggle with δ-ε definitions because they lack a habit of careful use of their native language?

I wouldn't say so. By studying linguistics on a deep level, this person learned to parse complicated multi-part statements and extract precise meaning from them. This skill--which people in general ...
user22788's user avatar
  • 854
12 votes
Accepted

Is 'For all $x$' an abuse of language in math?

No, there is no abuse of language here. $x$ and $y$ are placeholders that stand for individual numbers, and your second suggestion captures this: For each number we can insert in place of $x$ and $y$, ...
Natalie Clarius's user avatar
9 votes

What is this symbol called?

Please check the entire Greek alphabet, as you can find it in this Wikipedia page: https://en.wikipedia.org/wiki/Greek_alphabet. I must add that there are two ways to write the letter $phi$ in MathJax ...
Dominique's user avatar
  • 2,165
9 votes

What is this symbol called?

That's lowercase Greek phi, pronounced with an initial f sound and rhyming with English pie, lie or sky. That said, some speakers may pronounce it rhyming with English see, key or me. See https://en.m....
J W's user avatar
  • 4,753
9 votes

Is there any research on the impact of dismissive language (e.g., 'it's just...') in mathematics education?

Hypothetically, a study researching the effect of a single word ("just") within a complex educational context would fall under the heading of a psychological priming effect. In some sense, ...
Daniel R. Collins's user avatar
7 votes

Do undergraduates struggle with δ-ε definitions because they lack a habit of careful use of their native language?

The issue you raise is similar to those raised here: How to make students comfortable with the use of axiom of choice in analysis [Note: the question at the link has "axiom of choice" in the ...
user52817's user avatar
  • 11k
6 votes

Do undergraduates struggle with δ-ε definitions because they lack a habit of careful use of their native language?

I think the linguist is looking at it backwards: to study the formal grammar of a language, you have to apply some complex mathematical (or logical) ideas. Natural languages are imprecise, contextual, ...
IMSoP's user avatar
  • 161
5 votes

Do undergraduates struggle with δ-ε definitions because they lack a habit of careful use of their native language?

I think there are two (main) reasons why "people just blah, blah, blah, just talk away." One is linguistic: They have clear thoughts but cannot accurately express them in words. The other is ...
Andreas Blass's user avatar
5 votes

Is there any research on the impact of dismissive language (e.g., 'it's just...') in mathematics education?

In my experience (obviously anecdotal, but take from it what you will), it all comes down to whether you're dismissing the struggles of the student (i.e., "why is this not easy for you") vs ...
Justin Skycak's user avatar
5 votes

How should an educator answer a student who asks "Can this theorem be deduced in other systems of set theory?"

would it be fair to ensure that the course description and course syllabus include the name of the particular system of set theory that all theorems studied in the course are deduced from? No, ...
KCd's user avatar
  • 3,536
5 votes

Is 'For all $x$' an abuse of language in math?

I'm not a native english speaker, but I agree that "for all numbers $x$ and $y$" sounds strange. Because in everyday language we don't use names after a "for all". For instance, we ...
Michael Bächtold's user avatar
4 votes

Examples of different languages with mathematically different names for concepts

When I introduce the concept of an antiderivative in my calculus class, I mention that in my native German, it is called a Stammfunktion (stem-function, with "stem" as in "source", ...
Torsten Schoeneberg's user avatar
4 votes

Is 'For all $x$' an abuse of language in math?

The $x$ refers to the variable, i.e., the symbol '$x$', right? So, isn't For all real numbers '$x$',... a more accurate phrasing? If so, this sounds like For all real numbers the symbol $x,$.... ...
ryang's user avatar
  • 1,832
3 votes

Are some natural languages better for expressing mathematical concepts than others?

This question reminds me of the so-called Hopi time controversy. In 1958, Stuart Chase asserted (see page 3) that a person whose native language is Hopi has less trouble grappling with the "...
user52817's user avatar
  • 11k
3 votes

Are some natural languages better for expressing mathematical concepts than others?

Perhaps taking things to their extreme there are languages which lack simple numbering like the language of the Brazilian Amazonian people the Pirahã which appears to have only words for one and two (...
mdewey's user avatar
  • 311
3 votes

Is 'For all $x$' an abuse of language in math?

"For all 'things' $x$" is just the shortest way to say any of the following, which are equivalent but progressively wordy and cumbersome: "for all 'things' $x$" "if you ...
Justin Skycak's user avatar
3 votes

Is 'For all $x$' an abuse of language in math?

Do you have any qualms about "good old fashioned" first-order logic notation? In this language we would write something like $$ x,y\in \mathbb{R}\rightarrow P(x,y)$$ where, for example, $P(x,...
user52817's user avatar
  • 11k
3 votes

Do undergraduates struggle with δ-ε definitions because they lack a habit of careful use of their native language?

The is a built-in irreducible logical complexity in epsilon-delta definitions that has to do with the language of logic, rather than natural language. This has to do with alternations of quantifiers. ...
Mikhail Katz's user avatar
  • 2,238
2 votes

What is this symbol called?

For such a query, you might find it quicker to use one of the following tools: Google Image Reverse Search: Navigate to google.com and upload an image of the symbol. Google will display similar ...
LeafGlowPath's user avatar
2 votes
Accepted

Is there any research on the impact of dismissive language (e.g., 'it's just...') in mathematics education?

You can find one such study here: Kroeper, K. M., Muenks, K., Canning, E. A., & Murphy, M. C. (2022). An exploratory study of the behaviors that communicate perceived instructor mindset beliefs ...
Mahdi Majidi-Zolbanin's user avatar
2 votes

The word "numeral", is it being taught and does the word exist for it in your language?

I was taught "numeral" in the New Math era, and if you had asked me in my youth what it meant, I would have probably replied, "What? You mean like zero through nine?" In my mind, I ...
user1815's user avatar
  • 5,760
2 votes
Accepted

How should an educator answer a student who asks "Can this theorem be deduced in other systems of set theory?"

[Personal prelude: once in a model theory course we were being presented a proof of Ramsey's theorem, which I found very similar in spirit to some proofs of Bolzano-Weierstrass, so I mentioned it and ...
ac15's user avatar
  • 497
1 vote

Are some natural languages better for expressing mathematical concepts than others?

There is mathematics and then there is mathematics. Languages do presumably affect the speed at which children learn basic number words. It is known that children learn Danish (in general, not ...
Tommi's user avatar
  • 7,358
1 vote

Are some natural languages better for expressing mathematical concepts than others?

Let me give you an example in two languages: English (Dutch), and let's talk about tables (tafels [ˈtafəls]) and tables (tabellen [taˈbɛllən]): A table (tafel) is the piece of furniture at which you ...
Dominique's user avatar
  • 2,165
1 vote

Is 'For all $x$' an abuse of language in math?

edit - Stumbled on a succinct way to put it when writing the comments below: You're trying to apply a stricter reading of the English language than a reasonable speaker of the language would apply. ...
Flater's user avatar
  • 217

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