Naked Science Forum

General Science => General Science => Topic started by: talanum1 on 06/11/2021 17:56:16

Title: Is the Empty Set ={0}?
Post by: talanum1 on 06/11/2021 17:56:16

I have read that a sequence converges to a if a is an element of all U an element of O, in a topological space (S, O). Since the empty set must be in O there will never be such a. Does the empty set contain 0?

Title: Re: Is the Empty Set ={0}?
Post by: Bored chemist on 06/11/2021 19:07:30

Quote from: talanum1 on 06/11/2021 17:56:16

Does the empty set contain 0?

No, it's empty.

Title: Re: Is the Empty Set ={0}?
Post by: Eternal Student on 06/11/2021 20:49:03

Hi.

   I'm not sure what it was that you read there @talanum1.   It might have got a bit muddled up (maybe some symbols didn't display properly?)   However, I'd go along with Bored Chemist as regards the question in the title.

Best Wishes.

Title: Re: Is the Empty Set ={0}?
Post by: Bored chemist on 06/11/2021 21:33:38

"Is the Empty Set ={0}?"

No
It is not {0}.
The empty set is {}.

It is the set of current kings of the USA
It is the set of carrots on Mars

The number of things in the empty set is zero.
But zero is not in the empty set.

The set of (English names of)  months of the year has 12 members.
But 12 is not a month.