Sets and Operations on Sets
... A Venn Diagram is often used to show relationships between sets. At right is a Venn Diagram for two sets A and B. Anything inside the circle labeled A is considered part of set A and similarly for B. We shade in the section of the diagram we are interested in, so in the figure at left, we have shade ...
... A Venn Diagram is often used to show relationships between sets. At right is a Venn Diagram for two sets A and B. Anything inside the circle labeled A is considered part of set A and similarly for B. We shade in the section of the diagram we are interested in, so in the figure at left, we have shade ...
{ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 } A
... If you know that every member of B is also a member of D and you also know that there is at least one member of D that is not in B, you can use this symbol. In this case, B is called a PROPER SUBSET of D. ...
... If you know that every member of B is also a member of D and you also know that there is at least one member of D that is not in B, you can use this symbol. In this case, B is called a PROPER SUBSET of D. ...
Section 2.6 Cantor`s Theorem and the ZFC Axioms
... the sequences are zero. In other words Sequence 1 has 1’s in the 1st, 4th , and 6th position and zeros elsewhere. Sequence 2 has 1’s in the 3rd , 5th, 6th, and 9th positions and zeros elsewhere. Taking note of the positions of the 1’s, we can match any sequence of 0’s and 1’s subsets of the natural ...
... the sequences are zero. In other words Sequence 1 has 1’s in the 1st, 4th , and 6th position and zeros elsewhere. Sequence 2 has 1’s in the 3rd , 5th, 6th, and 9th positions and zeros elsewhere. Taking note of the positions of the 1’s, we can match any sequence of 0’s and 1’s subsets of the natural ...
Lecture Notes 2: Infinity
... The set S: the set of all and only ordinary sets, i.e. the set of all sets that are not elements of themselves. Question: Is S an ordinary set? If S is an ordinary set, then it contains itself as an element, since it is supposed to contain all ordinary sets. But that means that S is an extraordinar ...
... The set S: the set of all and only ordinary sets, i.e. the set of all sets that are not elements of themselves. Question: Is S an ordinary set? If S is an ordinary set, then it contains itself as an element, since it is supposed to contain all ordinary sets. But that means that S is an extraordinar ...
06. Naive Set Theory
... Then R is a set that belongs to itself. So R does belong to R. Russell’s Paradox is a paradox of the One and the Many: It looks like R can’t be thought of as a “one”. SO: Sets were introduced initially (in part) to address paradoxes of the Infinitely Big. But now it seems we’ve just replaced them wi ...
... Then R is a set that belongs to itself. So R does belong to R. Russell’s Paradox is a paradox of the One and the Many: It looks like R can’t be thought of as a “one”. SO: Sets were introduced initially (in part) to address paradoxes of the Infinitely Big. But now it seems we’ve just replaced them wi ...
sets and elements
... A set could have as many entries as you would like. It could have one entry, 10 entries, 15 entries, infinite number of entries, or even have no entries at all! For example, in the above list the English alphabet would have 26 entries, while the set of even numbers would have an infinite number of e ...
... A set could have as many entries as you would like. It could have one entry, 10 entries, 15 entries, infinite number of entries, or even have no entries at all! For example, in the above list the English alphabet would have 26 entries, while the set of even numbers would have an infinite number of e ...
First order theories
... But there exists first order theories defined by axioms which are not sufficient for proving all T-valid formulas. ...
... But there exists first order theories defined by axioms which are not sufficient for proving all T-valid formulas. ...
