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What do we mean by the word "distinct" in the first line of the first article Number in this book?

This is the line: "We say of certain distinct things that they form a group when we make them collectively a single object of our attention."

Example: Suppose a collection of three coins(may be of same or different value) in my pocket. I call the collection of these three coins A. Let's name the three coins C_1,C_2 and C_3. So A can be written as A={C_1,C_2,C_3}. Let C_1 and C_3 be of same value(say 1 rupee each). Are C_1 and C_2 still distinct from each other?

Does the word "distinct" have some other meaning in Fine's book as compared to the general meaning of the English word "distinct"?


Note: this question is also being asked at Math.SE
https://math.stackexchange.com/questions/732370/what-do-we-mean-by-the-term-number-of-things/743660#743660

  • The basic sense of "distinct" is "different". In the context of mathematics, we prefer the word "distinct" to "different". Also, those distinct objects don't have to be abstract ones. (Check out this Wikipedia page: en.wikipedia.org/wiki/Set_%28mathematics%29.) Above all, don't confuse the object itself with its value. If you have a set of three different (distinct) objects, it doesn't matter whether any two of them will share some properties or not. Objects are objects. Their properties (or values of their properties) are irrelevant to the discussion in the book. – Damkerng T. Apr 7 '14 at 10:13
  • Note the following link may help readers focus more on your question: books.google.com/… – CoolHandLouis Apr 7 '14 at 10:44
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In set theory, the only concern for "distinctness" is whether or not items have different names. Different names = Distinct.

Items can share a property (such as male/female or the value of a coin) and still be distinct items. Consider the following:

Set1 = {John, Joe, Mary}

We know John and Joe are "male" and "Mary" is female. Do we have three distinct "things"? Yes.

On the other hand, consider 3 people: Joe McDonald, Joe Harris, Jane Fonda. What is the set of all first names? It's {Joe, Jane}. There are only two distinct first names.

You have three different coins. They are distinct because each is a different coin and you gave each one a different name.

  • It should be noted that my question is not about set theory. I am asking for the general meaning of the word "distinct". Moreover the collection of coins in my pocket is not a set because coins are not abstract objects. – user31782 Apr 7 '14 at 9:07
  • Bytheway what are the properties of my coins which are distinct? How can you differentiate b/w two coins of same value, same wieght, same everything. Now you will say the coins are spatially distingiushable. Then consider a group {A,A,A} Would first A be distinct from the second A? – user31782 Apr 7 '14 at 9:12
  • A set does not have to contain abstract objects. You are not asking about the general meaning of "distinct"; you are asking about its meaning in the context of book on mathematics. If you want to generalize your question, you should remove that specific context :) – oerkelens Apr 7 '14 at 9:14
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    Oh I'm sorry. I thought you were asking for an answer related to the question you asked. Here's a great reference for general definitions (and much faster than asking here): lmgtfy.com/?q=definition+distinct – CoolHandLouis Apr 7 '14 at 9:39
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    @CoolHandLouis Maybe the problem isn't about "distinct". One possible problem is that the book has no definition of the word "thing(s)". What is "thing"? If we can be clear about what "thing" is, then we can be certain of what {A,A,A} is, and also the number of things in {A,A,A}. Without such a definition, we have a few choices, such as a) get along with the book, trying to make senses of it; b) argue that the book is wrong; or c) regard the book as a badly written one. That's my opinion. – Damkerng T. Apr 7 '14 at 19:30
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Does the word "distinct" have some other meaning in Fine's book as compared to the general meaning of the English word "distinct"?

Yes! When you have a math book, there are a lot of terms that become highly specialized jargon, and the words no longer mean what regular people might mean in English. (Logic classes also do this.)

So to understand the math book's usage, you have to look at what the book is defining "distinct" to mean, in that distinct (ha!) case. So when you look it up in the dictionary (e.g., dictionary.reference.com ), you go looking to see if there is a "math" definition. In the case of http://dictionary.reference.com/browse/distinct , I scroll waaaaay down and it says: "(maths, logic) (of a pair of entities): not identical". As you can tell by the term "maths" instead of "math," that's a British definition. Since you're working from an older book, perhaps less deviated from British English (or written by a British author in the first place), the chances are high that that's the definition you want.

  • I could not find the "math" definition in that link. – user31782 Jan 28 '15 at 10:25
  • Are C_1 and C_2 distinct from each other? – user31782 Jan 28 '15 at 10:28
  • 1: The "math" definition is in that link, very near the bottom. I just found it there again. Use your browser's "search" function to search for the word "Math" and you will find it. 2: Probably, because of the _1 and _2 components, but you'll have to see if your book defines them as distinct in whatever math problem it has. I have forgotten most math past simple algebra, so look for a mathematics expert for math answers. – A.Beth Jan 28 '15 at 22:57

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