Understanding ⊂ & ⊆ for the Puzzled

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The symbols ⊂ and ⊆ are often used interchangeably to indicate that all elements of set A are contained within set B. However, some authors differentiate between them, using ⊂ to signify that A is a proper subset of B, meaning A is not equal to B. It's essential to refer to the specific conventions used in your textbook for clarity. Understanding these distinctions can help avoid confusion in set theory discussions. Familiarity with the author's notation will enhance comprehension of the material.
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What is the difference between using ⊂ and ⊆? My book was not particularly lucid on this topic.
 
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Bashyboy said:
What is the difference between using ⊂ and ⊆? My book was not particularly lucid on this topic.

Depends on the author. Usually, the two notations mean the same thing, that is: A\subset B or A\subseteq B means that all elements in A are also in B.

Other authors (but a minority!) use A\subset B to mean that A is a subset of B but A is not equal to B.

You should check your book to see which convention he uses.
 

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