Subsets and Supersets, Revisted

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Subset:

If A is a subset of B, but A is not equal to B (i.e. there exists at least one element of B which is not an element of A), then

• A is also a proper (or strict) subset of B;
• or equivalently
  • B is a proper superset of A;

With that in mind-

Take two sets:

{0,1,2,3,...}   and    {1,2,3,4,...}

It has been stated and agreed that the first set is a proper superset of the second and the second set is a proper subset of the first.

Given the above definition, what does that tell you about the two sets?

It tells you that the first set has at least one element that the second set does not, ie they are not equal- MEANING EQUAL IN SIZE MORONS.

So if two sets are not equal (MEQANING EQUAL IN SIZE), then they cannot have the same cardinality. And if we look at Cardinality, we read that:

Some infinite cardinalities are greater than others.

Greater than is NOT equal to. So infinite sets are not necessarily equal, ie do not necessarily have the same cardinality.

Go figure...

Great Neil Rickert chimes in with his usual bald assertion and false accusation and no proof.

Can we see the proof that {0,1,2,3,...} is the same size as {1,2,3,4,...}. And please have that proof explain the obvious contradiction noted above.

And oleg chimes in with the lie that I have seen the "proof". Add mathematical proof to the long list of things oleg doesn't understand.

Oleg, your "proof" is refuted by the explanation in the above post.