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No, the size of infinities vary! Some are smaller than others.
Eg: the size of the set of numbers between 0 and 1 is infinite (0.1,0.11 and so on), but the size of this infinity is different from the size of the set of all numbers.
This is very very complicated maths and even the greatest mathematicians have avoided this paradox.
I don't know the proof well so just search around the net for it.
In mathematics, there are at least two categories of infinite sets - countably infinite, and uncountably infinite. Countably infinite means that you can set up a one to one correspondence between all members of the set and the set of natural number, aka "counting numbers".
Integers are countably infinite. You can pair them up with the natural numbers thus: 1,0 2,-1 3,1 4,-2 5,2 6,-3 and so on. The set of even numbers, odd number, and rational numbers are all countably infinite. The set of Real numbers, however is uncountably infinite. It can be shown that you can identify at least one real number that is not included in the set when you try to count all real numbers - thus while there are an infinite number of integers, there are even MORE real numbers. Not all infinite sets have the same number of elements.
What else can I help you with?
What is the relationship of number of elements to number of subset?
A finite set, with n elements has 2n subsets, including the empty set and itself. For infinite sets the number of subsets is the same order of infinity.
What are the finite or infinite sets?
A finite set is one containing a finite number of distinct elements. The elements can be put into a 1-to-1 relationship with a proper subset of counting numbers. An infinite set is one which contains an infinite number of elements.
When are two sets equivalent?
Two sets are considered equivalent when they contain the same number of elements, regardless of whether the elements themselves are the same or the order in which they are listed. This means there exists a one-to-one correspondence (bijective function) between the elements of the two sets. It’s important to note that equivalent sets can be of different types, such as finite and infinite sets, as long as their cardinalities match.
What is the meaning of equivalent set?
Equivalent sets are sets with exactly the same number of elements.
What is the meaning of of infinite sets?
Infinite sets are collections of elements that have no finite number of members. They can be countably infinite, like the set of natural numbers, where elements can be listed in a sequence, or uncountably infinite, like the set of real numbers, which cannot be matched one-to-one with natural numbers. The concept of infinite sets challenges our understanding of size and quantity in mathematics, leading to various paradoxes and deeper explorations of set theory. These sets play a crucial role in various fields, including mathematics, physics, and computer science.
What are kinds of sets according to number of elements what are kinds of sets according to number of elements?
Finite, countably infinite and uncountably infinite.
What is the cardinality of a union of two infinite sets?
The cardinality of finite sets are the number of elements included in them however, union of infinite sets can be different as it includes the matching of two different sets one by one and finding a solution by matching the same amount of elements in those sets.
What is the relationship of number of elements to number of subset?
A finite set, with n elements has 2n subsets, including the empty set and itself. For infinite sets the number of subsets is the same order of infinity.
What are the kinds of sets according to number of elements?
One possible classification is finite, countably infinite and uncountably infinite.
What are the finite or infinite sets?
A finite set is one containing a finite number of distinct elements. The elements can be put into a 1-to-1 relationship with a proper subset of counting numbers. An infinite set is one which contains an infinite number of elements.
When are two sets equivalent?
Two sets are considered equivalent when they contain the same number of elements, regardless of whether the elements themselves are the same or the order in which they are listed. This means there exists a one-to-one correspondence (bijective function) between the elements of the two sets. It’s important to note that equivalent sets can be of different types, such as finite and infinite sets, as long as their cardinalities match.
Two sets that contain the same number of elements are called what?
Two sets that contain the same number of elements are called "equinumerous" or "equipollent."
What is meaning of equivalent sets?
Equivalent sets are sets with exactly the same number of elements.
What is equal set from equivalent sets?
equal sets with exactly the same elements and number of elements.equivalent sets with numbers of elements
What is the meaning of equivalent set?
Equivalent sets are sets with exactly the same number of elements.
When you have to say that a give sets is infinite and empty-set?
A set is infinite if it has infinitely many elements in it.
What is the meaning of of infinite sets?
Infinite sets are collections of elements that have no finite number of members. They can be countably infinite, like the set of natural numbers, where elements can be listed in a sequence, or uncountably infinite, like the set of real numbers, which cannot be matched one-to-one with natural numbers. The concept of infinite sets challenges our understanding of size and quantity in mathematics, leading to various paradoxes and deeper explorations of set theory. These sets play a crucial role in various fields, including mathematics, physics, and computer science.
