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I was wondering if figure, number, digit and other similar words can be used interchangeably in mathematics? What are the differences in their usage?

How about if we extend these notions to other contexts, such as in computer science, and in life more generally speaking?

Thanks and regards!

FD_bfa
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Tim
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    Number and digit cannot be used interchangeably; in ordinary decimal notation, there only ten digits, but infinitely many numbers. "Figure" usually refers to geometric figures rather than numbers; so, no. As for what happens in CS and in life, those are outside the scope of this site. – Arturo Magidin May 02 '11 at 02:43
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    @Arturo, "figure" often refers to numbers, as in "I added up this column of figures $5$ times - and here are the $5$ answers I got." But as "number" can't refer to geometric figures, the two words are certainly not always interchangeable. – Gerry Myerson May 02 '11 at 02:49
  • @Gerry: Thanks; I am aware of the use of "figure" for number, but it seems to be becoming more uncommon these days in ordinary language, and in my experience it is extremely rare of "in mathematics". – Arturo Magidin May 02 '11 at 02:53
  • @Gerry: I only compare their similar meanings. My questions might seem stupid, but it took me a while to realize "figure" means number not graph when reading some math related material found from internet. So I was wondering if such usage is acceptable. @Arturo: Nice to know your experience. – Tim May 02 '11 at 02:54
  • @Tim: As a sort of analogy, digits are to numbers, what letters are to words. As Arturo points out, there are 10 digits, an infinitely many numbers, just as there are only 26 letters (52 if you count capital letters, too) in the English language, but many, many more words. Actually, I found the same analogy here: a short video on the difference between numbers and digits: http://www.youtube.com/watch?v=vBFxMndAUgw – amWhy May 02 '11 at 02:57
  • @Arturo: here is where I saw figure is used to mean number: 2nd line, page 2 of http://docs.google.com/viewer?a=v&q=cache:ip88a_Skz5AJ:www.richardclegg.org/networks2/Worksheet2_06.pdf+m/m/1/2+queueing&hl=en&gl=us&pid=bl&srcid=ADGEESgYkACpxXcr2NnfPe6faKIVHyhyOtG_uxhLG06RTUywSzCC-BFgZFNnlHF1O20C-s6rjr8mKVoqwXmgAAui18Y0yXpKt0a8pH97zOkrUhqxBzzfwdCqb_APrUG3mW-wwiExTbZP&sig=AHIEtbR4DyK2iB8UOO9OydDApkeP1QcFZQ "The final figure 2 means that at most two customers are allowed in the system". – Tim May 02 '11 at 03:05
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    @Arturo: Well, there is the expression "significant figures". :) – J. M. ain't a mathematician May 02 '11 at 03:09
  • @J.M.: Where it is used in place of "digit", not "number". (-: – Arturo Magidin May 02 '11 at 03:11
  • @Tim: You're right: there is ambiguity with respect to the distinction (number, digit, figure); I think we're just trying to point out some good ways to differentiate their uses. The English language, though, is often ambiguous, and so you need to take the context into consideration. "Figure" is used in math texts, as it is in your text on Google.docs, and many other places, to refer to a table, chart, graphic, drawing, data, demonstration, etc. How it's being used, and what it means, may need to be gleaned from the context. Also, would it help to think of digits as "numerals"? – amWhy May 02 '11 at 03:15
  • Anyway, to make @Amy's statement more accurate: "there are 10 digits in the decimal number system". In binary, the only digits you have are 0 and 1, and similarly for other base-$b$ number systems. – J. M. ain't a mathematician May 02 '11 at 03:16
  • @Amy: Thanks! I was more concerned about if using figure as number is proper in mathematics. – Tim May 02 '11 at 03:17

2 Answers2

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Let's first define the $3$ terms that you refer to in your question, and then we can look at some examples to illustrate any differences between them.

Number: a mathematical object used to count, measure, or label.

Figure: a number (commonly used in an applied setting such as statistics relating to the performance of a company).

Digit: any of the numerals from $0$ to $9$.

Numbers are very broad and so they include any integer, decimal number, fraction, negative number, or complex number. Some examples include $4, 52, 7.5, (-3),$ and $(5+3i)$.

Any of the above numbers could be referred to as figures. However, it is much more common for the term "figure" to refer to quantities in context, such as profit, loss, height, rates of change, etc. Some examples include $ {$} 1000, 112$%,$-£40$, etc. Figures are usually presented as tables but can also be expressed using diagrams, graphs, or charts (which are, somewhat confusingly, also referred to as "figures").

Finally, digits are any of the following numbers: $0,1,2,3,4,5,6,7,8,9$. There are exactly $10$ digits and so it is much clearer what we mean by these than the previous two terms.

FD_bfa
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In addition to the answer above - I would suggest that when discussing numbers we need to be careful to think first whether we are using cardinal numbers (to measure the size of something) or ordinal numbers (to measure the position of something).

With finite numbers, there is not too much of an issue, but there may be an issue if the word number is used to refer to a transfinite number.

Figures are often a lazy term for descriptive statistics.

Red Five
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