Thread: The set (n) and (x) where n*x=x.

The set of real numbers (n), and any real number (x), where n*x=x.
I guess that the only answer is that the set (n) consist's wholly of the number one. Can a set contain only one number?
I'm also pretty sure that I haven't used proper set notation. What's the proper way to express the above statement?
8)

Sets can contain 0 or more elements, and are typically denoted with curly braces {}.

Thank's. 8)

Originally Posted by GiantEvil

The set of real numbers (n), and any real number (x), where n*x=x.
I guess that the only answer is that the set (n) consist's wholly of the number one. Can a set contain only one number?
I'm also pretty sure that I haven't used proper set notation. What's the proper way to express the above statement?
8)

yes, this is only true where both n and x are 1.

Originally Posted by GiantEvil

The set of real numbers (n), and any real number (x), where n*x=x.
I guess that the only answer is that the set (n) consist's wholly of the number one. Can a set contain only one number?
I'm also pretty sure that I haven't used proper set notation. What's the proper way to express the above statement?
8)

A set can can contain any non-negative cardinal number of elements. Including zero.

The set with zero elements is called the empty set.

Note that there are really two cases, and

If , you could express the set of which you speak in several ways:









If then the set is just the real numbers.

Sorry about the inaccurate notation. I meant {n} to be the set and "x" to be a variable.And I see that for {n}*x=x, x can be any real number if {n} contains a one. {n} can only be zero if x is also zero. Thank's guy's.

Originally Posted by DrRocket

A set can can contain any non-negative ordinal number of elements. Including zero.

Would that hold true even when it is a "set of" something within a specific group that is itself more abstract and conceptual?


Let's say I have 4 ideas. Clearly... I have a set of four which exist within the conceptual/abstract group of "ideas."

However, when I focus the set to exist within the group of "idea," zero doesn't seem to be valid... If I have no ideas, it would seem that I also do not have a "set of" them. Further, in common usage, a singular object like "one idea" would not seem to comprise a "set of" ideas. It's singular, so would seemingly be best described as "an" idea, instead of a set of them.

I know using the reals as noted in your post that what you've said is entirely valid, and I also concede that at present your knowledge of math structures and language far surpasses my own. However, I wonder if when you expand the question beyond pure math if your response still holds.

Any thoughts? I ask, because IINM the OP was inspired by a thread religious in nature in which I was a participant, where I made a comment regarding non-belief and an assertion that one belief is not the same as a set of them.

Originally Posted by inow

Originally Posted by DrRocket

A set can can contain any non-negative ordinal number of elements. Including zero.

Would that hold true even when it is a "set of" something within a specific group that is itself more abstract and conceptual?


Let's say I have 4 ideas. Clearly... I have a set of four which exist within the conceptual/abstract group of "ideas."

However, when I focus the set to exist within the group of "idea," zero doesn't seem to be valid... If I have no ideas, it would seem that I also do not have a "set of" them. Further, in common usage, a singular object like "one idea" would not seem to comprise a "set of" ideas. It's singular, so would seemingly be best described as "an" idea, instead of a set of them.

I know using the reals as noted in your post that what you've said is entirely valid, and I also concede that at present your knowledge of math structures and language far surpasses my own. However, I wonder if when you expand the question beyond pure math if your response still holds.

Any thoughts? I ask, because IINM the OP was inspired by a thread religious in nature in which I was a participant, where I made a comment regarding non-belief and an assertion that one belief is not the same as a set of them.

I have no idea what you are talking about.

Sorry. I wasn't 100% sober, and simultaneously wanted to be cautious with my language so as not to turn a math thread into a religion thread. Mea culpa.

I made a comment that atheism is not a set of beliefs as a response to someone who had asserted the opposite. I asked them to name which beliefs come from atheism. In response, they said, "lack of belief in god." I replied, "one belief does not make a set of them."

I might have been wrong, so am basically trying to check if your post above applies primarily to real numbers, and whether the logic involved might be different for more abstract concepts (like beliefs).

Do zero beliefs make a set of beliefs?
Does one belief make a set of beliefs?

Reading above, I'm inclined to think the answer is yes. I'm looking to do an accuracy check on that.

Originally Posted by inow

Do zero beliefs make a set of beliefs?
Does one belief make a set of beliefs?

Reading above, I'm inclined to think the answer is yes. I'm looking to do an accuracy check on that.

In terms of mathematics the answers are "yes" and "yes".

However, in mathematics a "set" is nothing but a collection of things called elements, basically a box of stuff, and the box is allowed to be empty. There are no restrictions whatever on the kind of stuff.

So, being a set is not much of a distinguishment.

Your debate seems to me to be more on the merits of the beliefs and whether or not you call them a set is unimportant. More important than whether they are a set is whether or not they are clearly defined for each individual claiming to adhere to them, self-consistent, logical, consistent with behavior, consistent with what is observed, etc. In a debate outside of mathematics one might expect that a "set of beliefs" would have these characteristics, and that the word "set" is more restrictive than when taken in the strict mathematical context.

The Library of Congress is a set of books. So is a box of copies of Mein Kamf. The intellectual value of the two sets is rather different.

A set can be any collection. A hammer, a stereo, a book and the star Betelgeuse constitute a set with four elements.

Mathematical terms are defined extremely precisely and therefore narrowly. That is necessary in mathematics, and it what gives mathematics its exactness and definitiveness. It is rarely the case that such precision in terminology is applied or even useful in non-mathematical discussions, and one should not assume that in such discussions a word carries its mathematical definition. It is probably better to assume that it takes on its dictionary definition, which is usually much less restrictive.

set (a group of things of the same kind that belong together and are so used) "a set of books"; "a set of golf clubs"; "a set of teeth"

Brilliant response, man. Thanks for that.