- published: 26 Aug 2011
- views: 70567343
In mathematics, an injective 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 mapped to by at most one element of its domain. If in addition all of the elements in the codomain are in fact mapped to by some element of the domain, then the function is said to be bijective (see figures).
An injective function is called an injection, and is also said to be a one-to-one function (not to be confused with one-to-one correspondence, i.e. a bijective function). Occasionally, an injective function from X to Y is denoted f: X ↣ Y, using an arrow with a barbed tail. The set of injective functions from X to Y may be denoted YX 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 nm (see the twelvefold way).
A function f that is not injective is sometimes called many-to-one. (However, this terminology is also sometimes used to mean "single-valued", i.e., each argument is mapped to at most one value; this is the case for any function, but is used to stress the opposition with multi-valued functions, which are not true functions.)
Beyoncé - 1+1
League of Legends - SKT vs. TSM - IEM Katowice 2016 - Semifinal Map 1
The Division Walkthrough Gameplay Part 1 Campaign & Dark Zone
Soccer Sunday : 2016 Week 1 Live Show
WELCOME BACK FRIENDS!! | Five Nights at Candy's 2 - Part 1
Don't set your iPhone's date to January 1, 1970! The fastest way to BRICK an iPhone!!!
Eat Bulaga KalyeSerye March 1 2016 AlDub Day 192 #ALDUBBirthdayWish
1 MILLION SUBSCRIBERS! FUNnel Vision Gets Fit + Donut Challenge Family Battle (Taste Test Game)
Barcelona vs Rayo Vallecano 5-1 All Goals 3-3-2016 HD
TSM vs OG (Bo1) | IEM KATOWICE 2016 | IEM Season X World Championship | Team SoloMid vs Origen
LEVEL 1 | LET’S PLAY DOCTOR
Eat Bulaga March 1 2016 Juan for All - All for Juan Sugod Bahay
One Direction - History (Official Video)
Jillian Michaels 30 Day Shred: Level 1