Ok with the sets provided by studiot, thats technically not something from nothing because the brackets exist. Where did the brackets come from?

 

Could you elaborate on your statement? How did you get something from nothing?

Ok with the sets provided by studiot, thats technically not something from nothing because the brackets exist. Where did the brackets come from?

 

Could you elaborate on your statement? How did you get something from nothing?

 

 

Look more closely at my previous post.

 

Point 1 states quite clearly: start with the set with no members and I used the conventional symbol for this -

 

[math]\emptyset [/math]

 

 

It is officially called the empty set and is literally nothing. Note there are no brackets.

 

This is the first term in the sequence.

 

Now point 2 describes how to create the sequence.

 

The brackets are a common mathematical notation for enclosing the specification of a set. This can either be by enumerating all the members, as I have done, or by providing a rule or formula for identifying members.

 

Create a set that does have members, in fact create a sequence of sets linked by the rule that each succeeding term contains all the previous terms as members. So each term is a set with one more member than the previous term.

 

To show they are sets enclose them in brackets.

 

So the second term in the sequence is a set with precisely one member. This member is the empty set described above.

 

The next term has one more member, ie precisely two members and these are the empty set and the set with one member.

 

the next term has one more member, ie precisely three members and these are the empty set, the set with one member and the set with two members.

 

You can, of course, proceed indefinitely with this process. And each term is constructed from - nothing.

Edited May 13, 201312 yr by studiot