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What is the largest number in a data set?
It's the maximum.Probably C, the continuum.The cardinality (count) of the infinite set of integers is Aleph-null. Then C = 2^(Aleph-null).
What are the classifications of a set?
Sets are classified according to their cardinality: a measure of the number of elements that it contains. The cardinality of a set may be finite, aleph-null or aleph-one. Aleph-null is the number of integers (or rational numbers). Aleph-one
Can infinity be an element of a set?
Yes.The set of {Aleph-null, Aleph-one, ...}, which is the set of the different infinities, has infinity as an element.Aleph-null is the countable infinity.
What is that numbers of rational?
The number of rationals is Aleph-null.
Is infinity a real number?
Infinity is not a specific number but a cardinality. The cardinality of a finite set is the number of elements in the set. For example, the cardinality of the set {1, 2, 3, 4, 5} is 5. Simple enough, but what about the cardinality of all natural numbers? There is no end to natural numbers so the cardinality cannot be a number in the normal sense. The cardinality is an infinity, called aleph-null. [As an aside, aleph is the first letter of the Hebrew language – which, along with the next letter, beth, gives us the word alphabet.]The cardinality of any set which can be put into one-to-one correspondence with the set of natural numbers (or conversely) is also aleph-null. You then have the curious result that, using the mappings x-> 2x-1 and x -> 2x the cardinality of positive odd number is also aleph-null as is the cardinality of positive even numbers. Comparing cardinalities, you get the aleph-null + aleph-null = aleph-null or 2* aleph-null = aleph-null.This result can be extended to all integers so that n * aleph-null = aleph-null for all integers n. This leads to the counter-intuitive result that aleph-null * aleph-null = aleph-null! It is possible to devise a diagonal scheme which gives a one-to-one correspondence between all rational numbers and all natural numbers. So there are aleph-null rational numbers. The classic exposition for this is Hilbert’s Grand Hotel. See https://en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_HotelThe above sets are said to have countably infinite elements (since they can be put into 1-1 correspondence with the counting numbers.You may have noted that, when introducing aleph-null, I used the phrase “an infinity”. This is because there is another, higher cardinality: the uncountably infinite. The cardinality of the set of all subsets of a set with countably infinite elements, or 2-to-the-power-aleph-null. This infinity is also known as the continuum. Cantor proved that the cardinality of irrational numbers (and therefore the real numbers) is the continuum and also that there are no orders of infinity between aleph-null and the continuum.
What is a number for composite?
The cardinality of composite numbers is Aleph-null.
When was Aleph Zadik Aleph created?
Aleph Zadik Aleph was created in 1924-05.
When was Aleph Samach created?
Aleph Samach was created in 1893.
How can you find the total combination of positive and negative numbers?
Aleph-null (a listable infinity).
What is the thinking about The density of numbers on the number line of rational and irrational number?
There are countably infinite rational numbers. That is, it is possible to map each rational number to an integer so that the set has the same number of elements as all integers. This is the lowest order or infinity, Aleph-null. The number of irrationals is a higher order of infinity: 2^(Aleph-null). This is denoted by C, for continuum. There are no orders of infinity between Aleph-null and C.
When was The Aleph - short story - created?
The Aleph - short story - was created in 1945-09.
What is the highest place value in a decimal system?
The highest place value in the decimal system is the aleph null'th place. It should be noted that aleph null is an infinite number (in fact, it is the smallest infinity possible) and represents the cardinality of the natural number set. In other words, there is no finite number which is the highest place value in the decimal system. (The Aleph character breaks Answers.com's WYSIWYG editor. The Aleph null character looks like: 0א except that the 0 is on the other side of the aleph character )
