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A null set is a subset of every set

  1. May 26, 2014 #1
    Hi, I was wondering, how can a null set be a subset of other sets? Could anyone explain the idea in non technical terms, I'm just a beginner. :)

    Thank you!
  2. jcsd
  3. May 26, 2014 #2


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    Do you agree that "if A is NOT a subset of B then there an element in A that is not in B"?

    Do you see that, no matter what B is, the empty set cannot satisfy that?
  4. May 26, 2014 #3


    Staff: Mentor

    An interesting application of this is the construction of natural numbers via set theory:

    from wikipedia article:

  5. May 26, 2014 #4
    Well, I do understand your first part. Now, for the second part, are you saying that because the empty set has no elements, it can't satisfy(be a subset) of B?
  6. May 27, 2014 #5


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    The part that the empty set cannot satisfy is the "then there [is] an element in A that is not in B", with the empty set playing the role of A.
  7. May 27, 2014 #6


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    No, I'm saying the opposite of that. The first part was a condition for NOT being a subset of B. Since the empty set cannot satisfy it, the empty set must be a subset of B.
  8. May 27, 2014 #7

    Stephen Tashi

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    The first thing to understand is why a statement of the form "If A then B" is considered true when the statement A is false. (This is the way it is in mathematical logic - not in the way the man-in-the-street thinks about things.) There are many threads on the forum discussing this because most people find it a strange convention when they first encounter it. Do you understand why it is essential to have this convention in mathematics?
  9. May 28, 2014 #8
    I don't think it's all that strange.

    "If I win the lottery, I'll give you a million dollars". But I didn't win the lottery, so I never lied to you.
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