What is the difference between a "proper subset" and regular "subset" in mathematics?

Question

The sentence says "A is a proper subset of B if B contains at least one element not in A."

What is the difference between proper subset and a regular subset?

Answer 1

A subset of a set contains any or all of the elements of the set.

A proper subset contains any of the elements of the set but not all of them.

Answer 2

In other words, it's called a "proper" subset because it isn't the set itself.

The notation makes the distinction: A C B (here the "C" is the inclusion sign) means proper subset, i.e. A is not the same as B. But if you have a line under the inclusion sign (like a "C" underlined") this means "A is a subset of B", including the possibility that A may be the same as B.

Answer 3

First of all, what you need to understand is this; what are 'qualifications'? Generally speaking, a qualification is merely a piece of paper which shows how you or I have paid attention in class to what the 'teacher' tells us, and what the books we read 'tells' us. Then, come exam time, we merely regurgitate that which we have been 'told'. If, for instance, you answer a question or take an exam, and your answers are not what is 'required',..then you will 'fail'. Qualifications are NOT a measure of someones 'intelligence', it is merely a record of how well you have 'remembered' what you were required to remember while in education. Consider these thoughts, expressed by Albert Einstein: "Imagination is more important than knowledge." "The only thing that interferes with my learning is my education." Peace be upon you.