Sets

Dixon999 SG

wonder if there's ani difference between subset n proper subset? when 2 use subset n when 2 use proper subset to represent or can they be used interchangeably...can ani1 clear my doubts???

Arkansaw SG

first do you even know what is meant by proper subset

eagle SG

From Wiki, I bolded the important part

If A and B are sets and every element of A is also an element of B, then:
* A is a subset of (or is included in) B, denoted by $A \subseteq B$ .

If A is a subset of B, but A is not equal to B (i.e. there exists at least one element of B not contained in A), then
* A is also a proper (or strict) subset of B; this is written as $A\subsetneq B.$

wee_ws SG

Hi,

Interestingly, I have to use the concept of sets often in my research :)

Study sets well if you need to study mathematics at the university level!

Happy new year!

Cheers,
Wen Shih

wee_ws SG

Hi,

In my research, I deal with filters.

A filter is a non-empty set whose members are supersets of a particular given set. As an example, consider the set X = {1, 2, 3}. The filter generated by the set {1} has the following members: {1}, {1, 2}, {1, 3} and X.

Note that any filter is a subet of the powerset of X, whose members are the empty set, {1}, {2}, {3}, {1, 2}, {1, 3}, {2, 3} and X.

Thanks!

Cheers,
Wen Shih