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In mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers. [a] Equivalently, a set is countable if there exists an injective function from it into the natural numbers; this means that each element in the set may be associated to a unique natural number, or that the elements of the set can be counted one at a time ...
The best known example of an uncountable set is the set of all real numbers; Cantor's diagonal argument shows that this set is uncountable. The diagonalization proof technique can also be used to show that several other sets are uncountable, such as the set of all infinite sequences of natural numbers (see: (sequence A102288 in the OEIS)), and the set of all subsets of the set ...
The cocountable topology on a countable set is the discrete topology. The cocountable topology on an uncountable set is hyperconnected , thus connected , locally connected and pseudocompact , but neither weakly countably compact nor countably metacompact , hence not compact.
Donald Trump's pick for Commerce secretary underlined that broad country-by-country tariffs can be used to address a host of economic issues, including the protection of America's artificial ...
15 Big-Batch Dinners Perfect For Leftovers PHOTO: RACHEL VANNI; FOOD STYLING: ADRIENNE ANDERSON
When Kieran Culkin took the stage to accept the award for Male Actor in a Supporting Role for his work in A Real Pain, it was clear he hadn’t prepared a speech. “Thank you SAG-AFTRA for this ...
The concept of a "mass noun" is a grammatical concept and is not based on the innate nature of the object to which that noun refers. For example, "seven chairs" and "some furniture" could refer to exactly the same objects, with "seven chairs" referring to them as a collection of individual objects but with "some furniture" referring to them as a single undifferentiated unit.
The axiom of countable choice allows us to arbitrarily select a single element from each set, forming a corresponding sequence of elements (x i) = x 1, x 2, x 3, ... The axiom of countable choice or axiom of denumerable choice, denoted AC ω, is an axiom of set theory that states that every countable collection of non-empty sets must have a ...