MoronismJoin Date: 2010-02-08
Post Count: 451 |
Hello Off-Topic.
I am here to discuss mathematics with you....
We will discuss set-builder notation below:
Sets are merely mathematical "structures"/objects that enclose other mathematical objects.
Typical set notation is through the use of the curly-bracket characters, {}.
Sets are quite useful for modeling the properties of "concrete", real-world objects.
A sufficient example would be a young child's playpen. The playpen can contain many "toy" objects. Those "toy" objects are enclosed within the playpen. Hence, they are "elements" or "members" of the playpen.
Mathematically, we could express the playpen(And its elements) as this:
P = {Rubber Car,Brunette-Doll,Dinosaur};
"P" refers to the actual playpen set. All of the remaining names merely refer to the members of the playpen.
There is an inherent issue with the above: It assumes that all elements within the set are always toys. Well, since it is preferable to have only "child-safe" objects within a playpen, it is necessary to ensure that only permissible objects will be added into our set. The below example accomplishes this:
P = {o | T(o) = 1}
To a novice, the above may seem rather "complicated", though I assure you that the concept is actually much simpler than it appears.
"o" is the actual object that may become a member of playpen P. Function "T" accepts a object as its input and determines whether the input object is an actual toy.
If the object is a toy, 1 is the output value. If the object is not a toy, 0 is the output value.
Consequently, in this example, all objects that are toys(And consequently output 1) are enclosed within the playpen. Therefore, they are members of set P.
Mathematically, notation such as "x | condition" means in regular language that "all x values that fulfill a specific condition truthfully"
Hopefully this has provided an interesting subject to many users. |
|
AlphaerixJoin Date: 2014-07-26
Post Count: 6002 |
tl;dr |
|
|
agh stop im already going blank |
|
MoronismJoin Date: 2010-02-08
Post Count: 451 |
"tl;dr"
Why did you bother to provide a response then? |
|
MoronismJoin Date: 2010-02-08
Post Count: 451 |
As in the case of previous occasions, I did not specify the use of the terms "finite" and infinite in relation to set-notation.
The playpen above, "P", is finite. This is due to the fact that playpen "P" has a known limit of toys that it can contain.
Infinite sets, such as the the set of all integers, do not have any known limit. They are infinite. |
|
MoronismJoin Date: 2010-02-08
Post Count: 451 |
The classical "oven" is yet another of a finite set.
Imagine that we have an oven set, denoted by the uppercase character "O":
O = {Seasoned Carrots, Peanut-Butter Cookies, Baked Cod}
The above are merely consumable items within our oven. We could create function F to determine whether the food items are genuine members of our set in the acceptable form "F(o)=1"
"o" refers to our input object, as usual. 1 and/or 0 merely represent the food property of our object. If "0" is given as output, the state of the object is not an edible item. Otherwise, "1" is the valid state.
Let us try various other items(Note that "F" was chosen to represent the word "food":
F(Cake) = 1 -Edible!
F(Cupcake) = 1 --Edible
F(Lollipop) = 1 --Edible
F(Oil) = 0 --Not edible
F(Petroleum) = 0 --Not edible
F(Gasoline) = 0 --Not edible
Excellent data shown above. |
|
|
your doing it wrong i took discrete mathematical structures and i know your e wrong |
|
MoronismJoin Date: 2010-02-08
Post Count: 451 |
"i took discrete mathematical structures"
Describe the credibility of your course, as your instructor seems mistaken. |
|
|
i go to a ivy league school im on the league of legend team |
|
MoronismJoin Date: 2010-02-08
Post Count: 451 |
"i go to a ivy league school im on the league of legend team"
Ah, now I see.
Moving onward towards a central goal, is anyone else enjoying the discussion? |
|
|
I am englighted but What would happen if a sun made of ice would collide with a normal, lava-made sun? Both suns would be the same size and ice-made sun's temperature would be -1000 degrees of celsius and normal sun's temperature +1000 degrees of celsius.
Would their combined effects cancel each other out so that instead there would be only empty space or one 0-degree sun? |
|
MoronismJoin Date: 2010-02-08
Post Count: 451 |
Please maintain a certain extent relevancy while responding to my posts.
This thread is intended to provide educational value to an otherwise unspecific community. |
|
|
what your teaching is pseudoscien e |
|
MoronismJoin Date: 2010-02-08
Post Count: 451 |
"what your teaching is pseudoscien e"
Nonsensical statement. I am teaching unconventional set-theory.
Pseudoscience propagates false scientific methods. Unconventional scientific methods propagate scientific knowledge in a peculiar or otherwise unusual manner. |
|
|
like youre doing right now?? |
|
MoronismJoin Date: 2010-02-08
Post Count: 451 |
Well, is anyone interested? |
|
MoronismJoin Date: 2010-02-08
Post Count: 451 |
"Well, is anyone interested?"
Yes, I suppose so.
Common examples include dressers, boxes/crates, and closets. |
|