Why Every Set is a Subset of Itself | Set Theory

Why is every set a subset of itself? That's what we'll go over in today's set theory video lesson!

Let A and B be sets, then A is a subset of B if and only if every element of A is also in B. Certainly every element of A is in A, thus A is a subset of itself for any set A.

A proper subset of A is a subset of A that isn't equal to A. Thus, although every set is a subset of itself, NO set is a proper subset of itself.

I hope you find this video helpful, and be sure to ask any questions down in the comments!

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The outro music is by a favorite musician of mine named Vallow, who, upon my request, kindly gave me permission to use his music in my outros. I usually put my own music in the outros, but I love Vallow's music, and wanted to share it with those of you watching. Please check out all of his wonderful work.

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+WRATH OF MATH+

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[valnatasha.lorenzo]

I have an assignment and thanks to this now I understand clearly

[boojosissys]

an element of a set can never be a subset of itself? Is there any difference between every element is a subset of itself .and an element of a set can never be a subset of itself?

[PatriciaNzunda]

So, how do I prove it in an examination, a solution please😢

[EpicMathTime]

Ah, so every set is an element of itself. Got it.






_Disclaimer to the reader: that is axiomatically false, and is a joke._