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Suppose that one wants to define what it means for two sets to "have the same number of elements". One way to do this is to say that two sets "have the same number of elements", if and only if all the elements of one set can be paired with the elements of the other, in such a way that each element is paired with exactly one element.
However, this function is not injective (and hence not bijective), since, for example, the pre-image of y = 2 is {x = −1, x = 2}. (In fact, the pre-image of this function for every y, −2 ≤ y ≤ 2 has more than one element.) The function g : R → R defined by g(x) = x 2 is not surjective, since there is no real number x such that x 2 = −1.
The competition consists of 15 questions of increasing difficulty, where each answer is an integer between 0 and 999 inclusive. Thus the competition effectively removes the element of chance afforded by a multiple-choice test while preserving the ease of automated grading; answers are entered onto an OMR sheet, similar to the way grid-in math questions are answered on the SAT.
Satisfying properties (1) and (2) means that a pairing is a function with domain X. It is more common to see properties (1) and (2) written as a single statement: Every element of X is paired with exactly one element of Y. Functions which satisfy property (3) are said to be "onto Y" and are called surjections (or surjective functions).
In mathematics, an injective function (also known as injection, or one-to-one function [1]) is a function f that maps distinct elements of its domain to distinct elements of its codomain; that is, x 1 ≠ x 2 implies f(x 1) ≠ f(x 2) (equivalently by contraposition, f(x 1) = f(x 2) implies x 1 = x 2).
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Math League (grades 4–12) MATHCOUNTS; Mathematical Olympiads for Elementary and Middle Schools (MOEMS) Noetic Learning math contest (grades 2-8) Pi Math Contest (for elementary, middle and high school students) Rocket City Math League (pre-algebra to calculus) United States of America Mathematical Talent Search (USAMTS)
One-to-one (communication), the act of an individual communicating with another; One-to-one (data model), a relationship in a data model; One to one computing (education), an initiative for a computer for every student; One-to-one marketing or personalized marketing, an attempt to make a unique product offering for each customer