A set is a collection of objects called elements. They can be both finite and infinite.
A finite set will look something like this,
A = {1, 2, 3, 4, 5, 6, 7, 8, 9}
An infinite set will be like,
Z = {1, 2, 3, 4, …}
Coming to subsets, suppose if A is a subset of B then every element of A must also be in B. It is usually a set of positive integers that start from 1 to infinity. The dots indicate an implied pattern that goes on forever.
These are the Fundamental Notions of Sets.
Now let us consider some additional points–
Example –
{a, b, c, a, b, c} = {a, b, c}
Here the amount of numbers is not that important as all of them can be drawn into a single circle and only thing matter is what elements are written inside the circle.
Example –
{3, 2, 1} = {1, 2, 3} = {2, 1, 3}
Next important subtopic is that of Common Sets
N = {0, 1, 2, 3, …}  or, N = {1, 2, 3, 4, ….}
Mostly experts recommend using the set with natural number starting from 1 as these kinds of sets are more specific due to having Z+ positive integer.
These are a set of numbers which are either positive or negative and also whole numbers so they can go from negative infinity till positive infinity.
Example –
Z= {…, -2, -1, 0, 1, 2, …}
This is one fundamental notion that students needs to use a lot in discrete math.
It is kind of hard to list and mainly contains fractional numbers in a set.
Example –
Q = {1/1, ½, 1/3, 2/3, …}
Hence, rational numbers are any numbers that can be written as fractions.
This knowledge helps to find solution of the problem how many solutions are there to the equation x1+x2+x3+x4+x5=21?
For which the answer should be 106.
Now that we know what sets are along with the additional points about it, coming to the next topic,
Elements and cardinality
It talks about the things present in the sets and how big those sets are.
Sets need to be all mathematics, it can be words too that have meaning in the real world.
Example –
This is usually represented as yellow ∈ C
This is represented as green ∉ C.
This is symbolized as- lcl = 3
Which says that the cardinality of C is 3?
Knowing the answer of thee question how many solutions are there to the equation x1+x2+x3+x4+x5=21 cannot be impossible if one do not have the basic knowledge of discrete math.
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