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2. Ordinal number - Wikipedia

   en.wikipedia.org/wiki/Ordinal_number

   In set theory, an ordinal number, or ordinal, is a generalization of ordinal numerals (first, second, n th, etc.) aimed to extend enumeration to infinite sets. [ 1 ] A finite set can be enumerated by successively labeling each element with the least natural number that has not been previously used.

3. Even and odd ordinals - Wikipedia

   en.wikipedia.org/wiki/Even_and_odd_ordinals

   In fact, the even ordinal ω + 4 cannot be expressed as β + β, and the ordinal number (ω + 3)2 = (ω + 3) + (ω + 3) = ω + (3 + ω) + 3 = ω + ω + 3 = ω2 + 3. is not even. A simple application of ordinal parity is the idempotence law for cardinal addition (given the well-ordering theorem). Given an infinite cardinal κ, or generally any ...

4. Category:Ordinal numbers - Wikipedia

   en.wikipedia.org/wiki/Category:Ordinal_numbers

   Download as PDF; Printable version; In other projects ... Pages in category "Ordinal numbers" The following 51 pages are in this category, out of 51 total.

5. Zero-based numbering - Wikipedia

   en.wikipedia.org/wiki/Zero-based_numbering

   In a zero-based indexing scheme, the first element is "element number zero"; likewise, the twelfth element is "element number eleven". Therefore, an analogy from the ordinal numbers to the quantity of objects numbered appears; the highest index of n objects will be n − 1, and it refers to the n th element.

6. List of types of numbers - Wikipedia

   en.wikipedia.org/wiki/List_of_types_of_numbers

   Such a number is algebraic and can be expressed as the sum of a rational number and the square root of a rational number. Constructible number: A number representing a length that can be constructed using a compass and straightedge. Constructible numbers form a subfield of the field of algebraic numbers, and include the quadratic surds.

7. First uncountable ordinal - Wikipedia

   en.wikipedia.org/wiki/First_uncountable_ordinal

   Any ordinal number can be turned into a topological space by using the order topology. When viewed as a topological space, ω 1 {\displaystyle \omega _{1}} is often written as [ 0 , ω 1 ) {\displaystyle [0,\omega _{1})} , to emphasize that it is the space consisting of all ordinals smaller than ω 1 {\displaystyle \omega _{1}} .