The Set of all elements X ? What does this mean?

[leodvinci]

"The Set of all elements X" ? What does this mean?

I know it's really simple but I don't understand what it means. In set builder notation when I'm describing a particular set I know for example: {10,11,12,13,14,15} is {x |x is a whole number greater than 9 less than 16} and is read "the set of all elements x such that x is a whole number greater than 9 less than 16"
"EDITED"

What is this statement saying; I don't get it.

Is it just describing a set named x?
Like is "the set of all elements x" just saying that the elements of x are limited to a whole number greater than 9 less than 15.
So set builder notation is just giving a set a variable name and then describing the set?
Am I missing something or is it really that simple.

 

[Office_Shredder]

Threw notation is NOT defining a name for a set. If you write {x| x is between 9 and 15}, and them later say x has six elements, nobody will know what you are referring to. x here is basically a dummy variable in the notation, it refers to an arbitrary element of the set, not to the set itself. Furthermore the notation iss generally used so that once you have written this the variable 'x' no longer refers to anything at all unless you define it to. It is similar to dummy variables in integration

 

[Hawkeye18]

x is not a set, in your case it is a generic name for an element of the set

 

[oleador]

The notation {x | property of x} reads: the set of all x which have the stated property of x. From what I've read, it seems you understand what the notation means -- it is really that simple :)

Correction: it should be "less than 16" in your definition of the set.

 

[leodvinci]

Thanks for the quick responses.

Okay so; so if I understand this correct; Set builder notation describes the elements of a set as a variable. x itself it not a name for the set but It's describing numbers within a set.

The notation {x | property of x} reads: the set of all x which have the stated property of x. From what I've read, it seems you understand what the notation means -- it is really that simple :)

Correction: it should be "less than 16" in your definition of the set.

Your right; Thanks :-D

 

[oleador]

Okay so; so if I understand this correct; x itself it not a name for the set but It's an arbitrary number within a defined set.

Your intuition is correct. More precisely, x is a variable, and the set is a collection of all x's that satisfy the property specified in the definition of the set.

 

[leodvinci]

Your intuition is correct. More precisely, x is a variable, and the set is a collection of all x's that satisfy the property specified in the definition of the set.

Great; Thanks.
Now that I know this; I'm curious of the applications,situations or areas of math that is it useful?

 

[oleador]

Great; Thanks.
Now that I know this; I'm curious of the applications,situations or areas of math that is it useful?

The set notation is used ...everywhere. Open any more or less advanced math book (university level), and you will find this notation. A lot of mathematical results involve sets of numbers, functions, etc. The field that studies the properties of set is called Set Theory, and those properties are used widely in other branches of mathematics.

 

[leodvinci]

Thanks I really appreciate the response.
I'm an art major but I made it a goal to tackle my fear of math and make it sort of a hobby to start to fully understand and learn math. I've found it fun and interesting studying and solving problems using numbers.
This helped me a lot.