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

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.

• 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. Sep 12, 2019 at 12:49
• 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. Sep 12, 2019 at 18:27
• 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. Sep 12, 2019 at 18:32
• @TommiBrander thanks for your comment, that makes sense. I see what I can do about my question. Sep 15, 2019 at 7:55
• 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. Sep 24, 2019 at 20:39

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.

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).

In Mandarin Chinese,

• numeral: 数字
• number: 号码