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Basic Introduction Proper Subsets With Example Of Kids Math

Basic Introduction Proper Subsets With Example Of Kids Math

Basic Introduction Proper Subsets

Basic Introduction Proper Subsets:If we look at the definition of subsets and let our mind wander a bit, we come to a weird conclusion.

Let A be a set. Is every element in A an element in A? (Yes, I wrote that correctly.)
Well, um, yes of course, right?

So wouldn’t that mean that A is a subset of A?Basic Introduction Proper Subsets With Example Of Kids Math

This doesn’t seem very proper, does it? We want our subsets to be proper. So we introduce (what else but) proper subsets.

A is a proper subset of B if and only if every element in A is also in B, and there exists at least one element in B that is not in A.

This little piece at the end is only there to make sure that A is not a proper subset of itself. Otherwise, a proper subset is exactly the same as a normal subset.

Example: {1, 2, 3} is a subset of {1, 2, 3}, but is not a proper subset of {1, 2, 3}.
Example: {1, 2, 3} is a proper subset of {1, 2, 3, 4} because the element 4 is not in the first set.

If A is a proper subset of B, then it is also a subset of B.

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