CHAPTER - 01
SET THEORY
Part - 02
● Lets dive into the fascinating world of proper subsets Remember,
a subset is simply a collection of elements taken from a larger
set. But a proper subset, That's where things get interesting. It's
a subset that isn’t equal to the original set. Think of it like this: it's
a small piece of the larger set, but it's missing at least one
element. Crucially, we write it with a special notation signifying
that it's a proper subset. We don't use the equals sign = because,
by definition, a proper subset is not the same as the original set.
As our teacher, Sir Ji, emphasized, Proper not equal.
● To illustrate, let's say we have the set A = 1, 2, 3, 4. Now, let's
generate some proper subsets together, just like Sir Ji did with
his student.
★** ** The empty set is a proper subset; it contains no elements
from A.
★1, 2, 3, 4 These are all proper subsets, containing just one
element from A.
★1, 2, 1, 3, 3, 4 Combine pairs These are also proper subsets.
★And so on... we could continue generating all combinations of
elements.
● See how the possibilities rapidly increase. What about if our set
was a bit bigger Sir Ji cleverly used the example of the set 1, 2, 3
to highlight this. He cautioned that if we tried to list out all the
proper subsets for a set with even a moderate number of
elements, it would be very long.
SET THEORY
Part - 02
● Lets dive into the fascinating world of proper subsets Remember,
a subset is simply a collection of elements taken from a larger
set. But a proper subset, That's where things get interesting. It's
a subset that isn’t equal to the original set. Think of it like this: it's
a small piece of the larger set, but it's missing at least one
element. Crucially, we write it with a special notation signifying
that it's a proper subset. We don't use the equals sign = because,
by definition, a proper subset is not the same as the original set.
As our teacher, Sir Ji, emphasized, Proper not equal.
● To illustrate, let's say we have the set A = 1, 2, 3, 4. Now, let's
generate some proper subsets together, just like Sir Ji did with
his student.
★** ** The empty set is a proper subset; it contains no elements
from A.
★1, 2, 3, 4 These are all proper subsets, containing just one
element from A.
★1, 2, 1, 3, 3, 4 Combine pairs These are also proper subsets.
★And so on... we could continue generating all combinations of
elements.
● See how the possibilities rapidly increase. What about if our set
was a bit bigger Sir Ji cleverly used the example of the set 1, 2, 3
to highlight this. He cautioned that if we tried to list out all the
proper subsets for a set with even a moderate number of
elements, it would be very long.
