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I am a mathematics educator from Lithuania and I have recently realized that there is no separate word in our language for the word "numeral". To be more precise there is no term to describe the collection of symbols that uniquely identify a number. We only teach children the difference between a digit and a number. I believe that for this lack of terminology children are very likely to believe that a number is nothing more than a scribble on a piece of paper.

I have checked that in the English language the word "numeral" is used in two contexts:

  1. In linguistics to mean

    a numeral (or number word) in the broadest sense is a word or phrase that describes a numerical quantity. Wikipedia on "Numeral" in linguistics

  2. In mathematics to mean a collection of symbols to uniquely identify a number. Wikipedia on Numeral system

My question: in your country and language, is there a dedicated word to express the idea "a collection of symbols to uniquely identify a number"? If so, could you please write that word and also add whether it differs from the word the linguists use to mean "a word that describes a numerical quantity"? If the answer is no, it would still be interesting to hear it.

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    $\begingroup$ Welcome to ME.SE. I think an interesting question would be if teaching the distinction matters or not for some or any learning goals. Maybe this is what you really want to know? Another remark is that this question risks attracting a multitude of answers to the effect of "in my language..."; voting on them is not very meaningful. A better answer would provide some sort of synthesis or summary of several languages. $\endgroup$
    – Tommi
    Sep 12, 2019 at 12:49
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    $\begingroup$ Quoting from the quote of Genius: The Life and Science of Richard Feynman, during the New Math era the textbooks "placed a new emphasis on precise language: distinguishing “number” from “numeral,” for example, and separating the symbol from the real object. ... Feynman objected to a book that tried to teach a distinction between a ball and a picture of a ball — the book insisting on such language as “color the picture of the ball red.” He argued that mathematic language should strive for clarity, not pedantic precision. As for the word "numeral", you can always borrow it from another language. $\endgroup$
    – Rusty Core
    Sep 12, 2019 at 18:27
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    $\begingroup$ By the way, if you teach arithmetic starting from, say, live cows, then beads or sticks that represent (abstract) the cows, then group the sticks together meaning addition, then replacing one, two, three, etc. sticks with 1, 2, 3, etc, then formalizing grouping as "+"... So when you go all this way, kids do not have any problem internalizing that "1" is not a cosmic number but a representation of a quantity, and they don't need extra layer to explicitly abstract it out. $\endgroup$
    – Rusty Core
    Sep 12, 2019 at 18:32
  • $\begingroup$ @TommiBrander thanks for your comment, that makes sense. I see what I can do about my question. $\endgroup$
    – frombilas
    Sep 15, 2019 at 7:55
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    $\begingroup$ Although we have the word numeral in English, I doubt many people could tell you what it means as distinct from numbers. We do get taught though that there is more than one way of choosing to write numbers, either though different cultural systems or through using different bases. $\endgroup$
    – Jessica B
    Sep 24, 2019 at 20:39

4 Answers 4

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In the Yoruba Language, we use the word òǹkà to refer to tokens for representing numbers. Thus, it would correspond to the word numeral. The word òǹkà literally translates as 'that which is used for reckoning.' The prefix on (the n is a nasal) means thing, and the other part, ka, means to reckon, count, calculate, etc.

On the other hand the word number would correspond to iye, which may also mean amount or quantity.

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In English, mathematically speaking, "number" represents, in the "broadest sense," a word or phrase that describes a numerical quantity." That is, $0.5, \frac 12, \frac 48,$ one-half, etc., all represent the same number. That is, the number referenced here in my answer is represented by each and every member of the family of equivalent representations I list.

In Wikipedia, (English language), "numerals" are defined merely as "the symbols used to represent numbers". So each of member of the collection $0.5, \frac 12, \frac 48,$ and one-half, etc., are numerals, each representing the same unique number.

The distinction between "number" and "numeral" is not often made in the U.S. educational system. So it is not surprising to me that you have not encountered this distinction to be a significant educational focus in your experience here in the U.S.

Very roughly speaking, one helpful analogy, in linguistics, might be between syntax and semantics (compared to numerals and numbers, respectively): The term syntax refers to grammatical structure (mathematical symbols used, or numerals), whereas the term semantics refers to the meaning of the vocabulary symbols arranged with that structure (in mathematics, the number being represented by any of a number of equivalent representative numerals).

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In Mandarin Chinese:

  • number: 号数
  • numeral: 数字

Addendum (with assist from Justin Hancock)

What is the distinction between those words? Are "numbers" concepts related to quantity and "numerals" symbols used to represent numbers? Some sources online are suggesting that distinction, while others are suggesting they're synonymous.  -Joe

It isn't my native tongue, but to my understanding,

  • $\color{blue}号\color\red数$ (number) refers to a natural number or its value or count, whereas $\color\red数量$ means quantity. The character $\color\red数$ actually means ‘numerical/quantitative’. And, depending on the context, $\color\red数目$ means either number or quantity. Finally, $\color{blue}号码$ refers to a numerical code/identification/label, rather than a number in the mathematical sense.

  • $\color\red数\color{violet}字$ (numeral; synonym: $\color\red数目\color{violet}字$) refers to a natural number's symbolic representation. The character $\color{violet}字$ literally means the written word.

Hopefully more informative than confusing! Chinese is a rather fuzzy/flexible/non-absolute language indeed.

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  • $\begingroup$ What is the distinction between those words? Are "numbers" concepts related to quantity and "numerals" symbols used to represent numbers? I ask because I'm finding some sources online suggesting that distinction, and other suggesting they're synonymous (no distinction). $\endgroup$
    – Joe
    Oct 25, 2023 at 23:43
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    $\begingroup$ As a native speaker, 号码 does not mean “number” in the mathematical sense. Its use is restricted to numbers that are codes/labels, e.g. 电话号码, phone number, or 身份证号码, ID number. The word 数 is used for “number” in the mathematical sense. For example, even numbers are 偶数, real numbers are 实数, quaternions are 四元数. $\endgroup$ Oct 26, 2023 at 8:38
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    $\begingroup$ @Joe In principle, 数字 refers to the symbols used to represent a number, and 数 refers to a mathematical concept that represents a quantity, though quantity itself is a distinct concept. However, in colloquial speech, 数字 can be used synonymously with “number” similar to the English word “figure,” e.g. “数字再过一遍,” meaning “go over the figures one more time.” And numbers are sometimes conflated with their numerals, e.g. 一位数, “one-digit number,” which in Chinese and English both mean “a number whose numeral in a base-10 system has one digit.” $\endgroup$ Oct 26, 2023 at 9:08
  • $\begingroup$ The word 号数 is not that common, and it means something like “a number used to represent a type or grade.” For example, 型号 means model or type, as in car model, and 标号 means grade or rating, as in octane rating. If someone wanted to specifically refer to the numbers used and not the classifications that they signify, they could say 号数. To contrast with 数字, I would use either 数, which has the most general meaning of number, or 数目, which more specifically is used with amounts. I wouldn’t say 号数 or 数目 have to be natural numbers. $\endgroup$ Oct 26, 2023 at 11:54
  • $\begingroup$ Also to the original question’s point about the two meanings of “numeral” in English, we can say 数词 in Chinese to mean “number words.” For example, Chinese speakers learn that English has 基数词, cardinal numerals, and 序数词, ordinal numerals. $\endgroup$ Oct 26, 2023 at 11:58
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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 would have been thinking of the graphemes for zero through nine rather than the words or numbers, although I would not have had the pedantic precision to express that thought.

"Number" meant to me any quantity, whether numbers with units (signifying length, area, weight, money, etc.) or not. The fact that you could equate different numbers — eight quarters are two dollars — was just a cool game you could play with numbers.

Thus, "numeral" meant for me (and still does) the tokens used to express numbers (in the decimal system at first, and later in other bases). "Numeral" did not mean, nor does it now, "a word that describes a numerical quantity." If pressed, I would say that such a word is called the name of the number, but that's me searching for the nearest word I could quickly come up with. But I would not say that "zero point nine repeating," which describes the number 1 in the real-number decimal system, is the name of 1. The name of 1 is "one." The "digits of a number," which phrase I also learned in school, meant the (sequence of) numerals used to express the number. "A decimal point followed by infinitely many nines," for example.

Later, study in mathematics, computer science, and linguistics challenged some aspects of these conceptualizations for me. They allowed me to talk about numbers with enough pedantic precision (1) to wonder whether I'm speaking the same language as the rest of English-speaking Americans and (2) to be wrong instead of sort-of-right, esp. with regard to linguistics. Back to Feynman's execration of pedantic precision, excessively precise language does not sound like ordinary English to most teenagers in the U.S. It makes them doubt what you are saying, which is the opposite of what you're hoping to achieve. In mathematics, there are (it seems to me, if I'm not making a linguistics gaffe) different language-games for talking about "numbers." A discussion sometimes begins switching between them until the speakers find a common language-game. For instance, speaking with a student beginning calculus versus talking with someone who has had real analysis.

Finally, with respect to an implicit question in the OP's statement, "I believe that for this lack of terminology children are very likely to believe that a number is nothing more than a scribble on a piece of paper." Coincidentally, yesterday I was talking with a neuroscientist about mathematical concept development. It's not their area, and I was just looking for pointers on how to find out what is known. They made the point that there is evidence that the concepts that are learned early, even if not mastered, form a framework on which future knowledge will be built. Early learning informs their later learning. And those who are taught mathematical concepts underlying arithmetic do better later than those who are taught only how to do arithmetic, even if the ones taught concepts are not as proficient at calculating. So the question of whether a certain term could help lay a good foundation for understanding the concept of number seems important. I don't know that such a question has been investigated, so I can't give a scientific answer to it.

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