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Is the set of rational numbers is larger than the set of integers?
Yes, rational numbers are larger than integer because integers are part of rational numbers.
Are most numbers rational or irrational?
The set of irrational numbers is larger than the set of rational numbers, as proved by Cantor: The set of rational numbers is "countable", meaning there is a one-to-one correspondence between the natural numbers and the rational numbers. You can put them in a sequence, in such a way that every rational number will eventually appear in the sequence. The set of irrational numbers is uncountable, this means that no such sequence is possible. All rational and irrationals (ie real numbers) are a subset of complex numbers. Complex numbers, in turn, are part of a larger group, and so on.
Is every real number rational?
No. The set of real numbers contains an infinitely more irrational numbers than rational numbers.
What is complements of a set?
The complement of a set refers to everything that is NOT in the set. A "universe" (a set from which elements may be taken) must always be specified (perhaps implicitly). For example, if your "universe" is the real numbers, and the set you are considering is 0
Set of real numbers and set of complex numbers are equivalent?
Real numbers are a proper subset of Complex numbers.
Does the set of whole numbers is larger than the set of natural numbers?
If you mean larger by "the set of whole numbers strictly contains the set of natural numbers", then yes, but if you mean "the set of whole numbers has a larger cardinality (size) than the set of natural numbers", then no, they have the same size.
Is the set of rational numbers is larger than the set of integers?
Yes, rational numbers are larger than integer because integers are part of rational numbers.
What is the set of numbers including all irrational and rational numbers?
real numbers
Are most numbers rational or irrational?
The set of irrational numbers is larger than the set of rational numbers, as proved by Cantor: The set of rational numbers is "countable", meaning there is a one-to-one correspondence between the natural numbers and the rational numbers. You can put them in a sequence, in such a way that every rational number will eventually appear in the sequence. The set of irrational numbers is uncountable, this means that no such sequence is possible. All rational and irrationals (ie real numbers) are a subset of complex numbers. Complex numbers, in turn, are part of a larger group, and so on.
Is every real number rational?
No. The set of real numbers contains an infinitely more irrational numbers than rational numbers.
What is the set of numbers that includes all rational and all irrational numbers?
the set of real numbers
Derived Set of a set of Rational Numbers?
The derived set of a set of rational numbers is the set of all limit points of the original set. In other words, it includes all real numbers that can be approached arbitrarily closely by elements of the set. Since the rational numbers are dense in the real numbers, the derived set of a set of rational numbers is the set of all real numbers.
What is complements of a set?
The complement of a set refers to everything that is NOT in the set. A "universe" (a set from which elements may be taken) must always be specified (perhaps implicitly). For example, if your "universe" is the real numbers, and the set you are considering is 0
How can the set of real numbers be structured to show the elements that are included in the set?
It cannot be. The cardinality of the set of real numbers is the Continuum. This is greater than the total number of sub-atomic particles in the universe!
How and why are real numbers more difficult to represent and process than integers?
There are more real numbers than integers. The set of integers is countably infinite, of magnitude aleph-zero. The set of real numbers is uncountably infinite (specifically, aleph-one).A computer can't really represent real numbers (that would require an infinite amount of memory), rather, it uses an approximation.There are more real numbers than integers. The set of integers is countably infinite, of magnitude aleph-zero. The set of real numbers is uncountably infinite (specifically, aleph-one).A computer can't really represent real numbers (that would require an infinite amount of memory), rather, it uses an approximation.There are more real numbers than integers. The set of integers is countably infinite, of magnitude aleph-zero. The set of real numbers is uncountably infinite (specifically, aleph-one).A computer can't really represent real numbers (that would require an infinite amount of memory), rather, it uses an approximation.There are more real numbers than integers. The set of integers is countably infinite, of magnitude aleph-zero. The set of real numbers is uncountably infinite (specifically, aleph-one).A computer can't really represent real numbers (that would require an infinite amount of memory), rather, it uses an approximation.
Set of real numbers and set of complex numbers are equivalent?
Real numbers are a proper subset of Complex numbers.
The set of all rational and irrational numbers?
Are disjoint and complementary subsets of the set of real numbers.
