Names of large numbers

This article lists and discusses the usage and derivation of names of large numbers, together with their possible extensions.

The following table lists those names of large numbers which are found in many English dictionaries and thus have a special claim to being "real words". The "Traditional British" values shown are unused in American English and are becoming rare in British English, but their other-language variants are dominant in many non-English-speaking areas, including continental Europe and Spanish-speaking countries in Latin America; see Long and short scales.

English also has many words, such as "zillion", used informally to mean large but unspecified amounts; see indefinite and fictitious numbers.

Standard dictionary numbers

Apart from million, the words in this list ending with -illion are all derived by adding prefixes (bi-, tri-, etc., derived from Latin) to the stem -illion.Centillion appears to be the highest name ending in -"illion" that is included in these dictionaries. Trigintillion, often cited as a word in discussions of names of large numbers, is not included in any of them, nor are any of the names that can easily be created by extending the naming pattern (unvigintillion, duovigintillion, duoquinquagintillion, etc.).

Injective function

In mathematics, an injective function or injection or one-to-one function is a function that preserves distinctness: it never maps distinct elements of its domain to the same element of its codomain. In other words, every element of the function's codomain is the image of at most one element of its domain. The term one-to-one function must not be confused with one-to-one correspondence (aka bijective function), which uniquely maps all elements in both domain and codomain to each other, (see figures).

Occasionally, an injective function from X to Y is denoted f: X ↣ Y, using an arrow with a barbed tail (U+21A3 ↣ RIGHTWARDS ARROW WITH TAIL). The set of injective functions from X to Y may be denoted Y^X using a notation derived from that used for falling factorial powers, since if X and Y are finite sets with respectively m and n elements, the number of injections from X to Y is n^m (see the twelvefold way).

A function f that is not injective is sometimes called many-to-one. However, the injective terminology is also sometimes used to mean "single-valued", i.e., each argument is mapped to at most one value.