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In this table, The first cell in each row gives a symbol; The second is a link to the article that details that symbol, using its Unicode standard name or common alias. (Holding the mouse pointer on the hyperlink will pop up a summary of the symbol's function.);
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula.
However, one can effectively find notations that represent the ordinal sum, product, and power (see ordinal arithmetic) of any two given notations in Kleene's ; and given any notation for an ordinal, there is a recursively enumerable set of notations that contains one element for each smaller ordinal and is effectively ordered.
Ordinal indicator – Character(s) following an ordinal number (used when writing ordinal numbers, such as a super-script) Ordinal number – Generalization of "n-th" to infinite cases (the related, but more formal and abstract, usage in mathematics) Ordinal data, in statistics; Ordinal date – Date written as number of days since first day of ...
A form of unary notation called Church encoding is used to represent numbers within lambda calculus. Some email spam filters tag messages with a number of asterisks in an e-mail header such as X-Spam-Bar or X-SPAM-LEVEL. The larger the number, the more likely the email is considered spam. 10: Bijective base-10: To avoid zero: 26: Bijective base-26
Ordinal numbers: Finite and infinite numbers used to describe the order type of well-ordered sets. Cardinal numbers: Finite and infinite numbers used to describe the cardinalities of sets. Infinitesimals: These are smaller than any positive real number, but are nonetheless greater than zero.
The proof-theoretic ordinal of such a theory is the supremum of the order types of all ordinal notations (necessarily recursive, see next section) that the theory can prove are well founded—the supremum of all ordinals for which there exists a notation in Kleene's sense such that proves that is an ordinal notation.
The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics. Additionally, the subsequent columns contains an informal explanation, a short example, the Unicode location, the name for use in HTML documents, [ 1 ] and the LaTeX symbol.