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What is the equation for infinity?
Infinity is NOT a number, there is no FORMULA for it. Infinity cannot exist in any sets where it is defined. Infinities are different even for different sets! The infinity in natural numbers set {1, 2, 3, ...}, integers {0, 1, -1, 2, -1,....}, rational numbers {1/2, -1, 4/5,....}, real {pi, sqrt(2), 1, 4/5, ....}, the complex numbers {1, 5 +3i, ...} and many other infinite fields, rings, groups have their infinity defined as their "cardinality", or the abstract sense, the "size" of it. It quite obvious the infinity of natural numbers is much smaller than that of the real. It is said that the "cardinality" of the set of all "infinities" is the largest of all infinities. (Equal to the number of all possible sets). Why can't infinity be a number? Well, to be a "number" we must be able to add it together, and ta special element "0" such that "0" + a for any a is still a (or multiply, with element "1" instead, needed concept for concept of number, or number axioms). It's easy to prove that this element is UNIQUE, (or the equivalent class of it is unique, a and b are in the same equivalent class means a = b in the set) Now with our understanding and definition of infinity, "infinity" != 0, or that means there is no element in this set, we can't define operations within the empty set. But also, "infinity" + 1 = "infinity". We just said 0 is unique. Contradiction. So, no infinity is NOT a number. Please note, there is a difference between infinity as an ELEMENT then infinity as a NUMBER. An element of a set does not require to be part of the operation, this set will not be a well defined number set.
Which sets does the number zero belong?
There are an infinity of possible answers: the integers, rationals, reals, complex numbers, the set {0,1,-3}, the set containing only the element 0;
Does a set with no element belong to any kind of set?
I believe you are talking about subsets. The empty set (set with no elements) is a subset of any set, including of the empty set. ("If an object is an element of set A, then it is also an element of set B." Since no element is an element of set A, the statement is vacuously true.)
What is the set of all even natural numbers?
Infinity.
What is the supremum of empty set?
it's negative infinity!
What is the equation for infinity?
Infinity is NOT a number, there is no FORMULA for it. Infinity cannot exist in any sets where it is defined. Infinities are different even for different sets! The infinity in natural numbers set {1, 2, 3, ...}, integers {0, 1, -1, 2, -1,....}, rational numbers {1/2, -1, 4/5,....}, real {pi, sqrt(2), 1, 4/5, ....}, the complex numbers {1, 5 +3i, ...} and many other infinite fields, rings, groups have their infinity defined as their "cardinality", or the abstract sense, the "size" of it. It quite obvious the infinity of natural numbers is much smaller than that of the real. It is said that the "cardinality" of the set of all "infinities" is the largest of all infinities. (Equal to the number of all possible sets). Why can't infinity be a number? Well, to be a "number" we must be able to add it together, and ta special element "0" such that "0" + a for any a is still a (or multiply, with element "1" instead, needed concept for concept of number, or number axioms). It's easy to prove that this element is UNIQUE, (or the equivalent class of it is unique, a and b are in the same equivalent class means a = b in the set) Now with our understanding and definition of infinity, "infinity" != 0, or that means there is no element in this set, we can't define operations within the empty set. But also, "infinity" + 1 = "infinity". We just said 0 is unique. Contradiction. So, no infinity is NOT a number. Please note, there is a difference between infinity as an ELEMENT then infinity as a NUMBER. An element of a set does not require to be part of the operation, this set will not be a well defined number set.
Which sets does the number zero belong?
There are an infinity of possible answers: the integers, rationals, reals, complex numbers, the set {0,1,-3}, the set containing only the element 0;
How many infinity's are there?
There are an infinite number of infinities. The power set is the set of all subsets of a set. The power set of an infinite set is a larger infinite set. The first (smallest) infinite set is the integers: 1,2, 3, .... The second infinity is the set of real numbers. The third infinity is the set of all plane curves.
What is the set-builder notation of the problem the set of negative infinity and 0?
I think you mean zero to negative infinity is {x: x< or equal to 0}
When is an empty set an element of a set?
an empty set does not have any element
Does a set with no element belong to any kind of set?
I believe you are talking about subsets. The empty set (set with no elements) is a subset of any set, including of the empty set. ("If an object is an element of set A, then it is also an element of set B." Since no element is an element of set A, the statement is vacuously true.)
What is the set of all points outside of a circle?
Infinity
What is the set of all even natural numbers?
Infinity.
What is the supremum of empty set?
it's negative infinity!
Is the empty set an element of every set?
No. An empty set is a subset of every set but it is not an element of every set.
What is the element of a set?
element of a set is when two numbers are formed together to form a set and the element is based on a binary question or answer.
Is an empty set element of any set s?
The empty element is a subset of any set--the empty set is even a subset of itself. But it is not an element of every set; in particular, the empty set cannot be an element of itself because the empty set has no elements.
