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# Is null set proper subset of every set?

Wiki User

2012-04-21 10:43:36

First of all, the null set( denoted by is a subset of every set. But it being a proper set or improper set is debatable. Many mathematicians regard it as an improper set, and rightly have as when we say a set is a subset of another, the super set always contains at least one element. For eg,.

Let A be the set, in roster form we take it as:

A = {ϕ}, we clearly see n(A)=1

then P(A) = {ϕ,{ϕ}}

We observe that at least a set must have 1 element for it to have a proper set, but if we take A = ϕ ( i.e. n(A)=0), then clearly ϕ and A itself are improper sets of A and.

Hence the minimum amount of proper sets a set has is nil and improper is 2.

But I have seen a few high school text books who regard null set as a proper set, which is totally false, arguable by mathematicians, clearly signifying the lethargy of authors of the book failing to update their error driven books.

I assure you, that null set is an improper set of every set.

Wiki User

2012-04-21 10:43:36
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