What is the difference between a number and a numeral?

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A number is a concept that we have for some value. For example, hold out four fingers. You can conceive of the number four, you know how many are there. That is the number - more or less the concept you have in your mind.

A numeral is a name or a symbol for that concept. The symbol may be a 4 (in base 10) or a 100 (in base 2) or IV (if you are using Roman numerals) or |||| if you are using tally marks, etc. All of those symbols look different on paper. But the concept in your mind remains the same.

So a number may be expressed many different ways, using different numerals. But a numeral will always represent the same number, as long as you know what system (base, Roman, tally, etc.) you are using.

It might help to think of it like languages. For example, a “book” is a word for that thing you read, with many pages. In German, it’s a “Buch,” in French it’s a “libre,” in Spanish it’s a “libro,” and in Vulcan it’s, well, I don’t know what it is in Vulcan, but you get the picture. They are all different words for the same Idea. The book is the actual object, but “book,” “Buch,” “livre” and “libro” are simply words, or names for the object.

So you might consider numbers to be the Ideas, and numerals to be the names for the Ideas.

Of course, as always, there are more in-depth ways to look at this issue, but the above should give you a good, working basis to explore further, if you wish.

I hope this gave you something to think about, 

Your pal, 

Brian

Tags: numbers , numerals