**Examples**

- The set {1, 2} is a proper subset of {1, 2, 3}.
- Any set is a subset of itself, but not a proper subset.
- The empty set { }, denoted by ∅, is also a subset of any given set
*X*. It is also always a proper subset of any set except itself. - The set {
*x*:*x*is a prime number greater than 10} is a proper subset of {*x*:*x*is an odd number greater than 10} - The set of natural numbers is a proper subset of the set of rational numbers and the set of points in a line segment is a proper subset of the set of points in a line. These are examples in which both the part and the whole are infinite, and the part has the same number of elements as the whole; such cases can tax intuition.

Read more about this topic: Subset

### Famous quotes containing the word examples:

“In the *examples* that I here bring in of what I have [read], heard, done or said, I have refrained from daring to alter even the smallest and most indifferent circumstances. My conscience falsifies not an iota; for my knowledge I cannot answer.”

—Michel de Montaigne (1533–1592)

“No rules exist, and *examples* are simply life-savers answering the appeals of rules making vain attempts to exist.”

—André Breton (1896–1966)

“Histories are more full of *examples* of the fidelity of dogs than of friends.”

—Alexander Pope (1688–1744)

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