Concept
Instant-runoff voting (IRV) is an electoral system designed to ensure that the winning candidate achieves a majority by allowing voters to rank candidates in order of preference. If no candidate secures a majority in the first round, the candidate with the fewest votes is eliminated, and their votes are redistributed based on the voters' next preferences, a process that repeats until one candidate achieves a majority.
Concept
A function is a fundamental concept in mathematics and computer science that describes a relationship or mapping between a set of inputs and a set of possible outputs, where each input is related to exactly one output. Functions are used to model real-world phenomena, perform calculations, and define operations in programming languages, making them an essential tool for problem-solving and analysis.
Concept
In various fields, 'domain' refers to a specific area of knowledge or activity, characterized by its own set of rules and conventions. Understanding the domain is crucial for effective problem-solving and communication within that context.
Concept
In mathematics, the codomain is the set into which all outputs of a function are constrained to fall, effectively defining the range of possible values the function can produce. It is important to distinguish between the codomain and the range, as the range is the actual set of values that the function maps to within the codomain.
Concept
An image is a visual representation of an object, scene, or concept, captured or created through various mediums such as photography, painting, or digital technology. It serves as a powerful tool for communication, allowing for the conveyance of complex ideas, emotions, and information in a form that can be universally understood.
Concept
Mapping is a process of creating a visual or symbolic representation of relationships, data, or geographical areas to facilitate understanding and analysis. It is widely used across various fields such as geography, mathematics, and data science to translate complex information into an accessible format.
Concept
A continuous function is one where small changes in the input lead to small changes in the output, ensuring there are no sudden jumps or breaks in its graph. Continuity is a fundamental property in calculus and analysis, crucial for understanding limits, derivatives, and integrals.
Concept
A discrete function is defined only for specific, distinct values, often integers, and is not continuous over any interval. It is often used in contexts where data is countable and can be represented as a sequence of points on a graph, such as in time series or digital signals.
Concept
Interval notation is a mathematical notation used to represent a range of values, typically numbers, as an interval on the real number line. It uses brackets and parentheses to indicate whether the endpoints are included or excluded, providing a concise way to express inequalities and solutions to equations.
Concept
Set notation is a mathematical language used to describe and define collections of objects, typically numbers, in a clear and concise manner. It allows for the expression of complex relationships and operations on sets, facilitating a deeper understanding of mathematical structures and logic.
Concept
A surjective function, or onto function, is a type of mapping between two sets where every element in the codomain has at least one pre-image in the domain. This ensures that the function covers the entire codomain, making it an essential concept in understanding the structure and behavior of mathematical functions.
Concept
An injective function, also known as a one-to-one function, ensures that distinct inputs map to distinct outputs, meaning no two different elements in the domain are mapped to the same element in the codomain. This property is crucial for establishing a function's invertibility on its image, as it guarantees a unique inverse function can be defined for the range of the injective function.
Concept
A bijective function is a mathematical function that is both injective (one-to-one) and surjective (onto), meaning each element of the function's domain maps to a unique element of its codomain, and every element of the codomain is mapped by some element of the domain. This property ensures that a bijective function has an inverse function, which uniquely reverses the mapping process.
Concept
An unbounded function is a type of mathematical function that does not have finite upper or lower limits in its range, meaning it can take on arbitrarily large or small values. This characteristic is crucial in understanding the behavior of functions in calculus and real analysis, especially in the study of limits and asymptotic behavior.
Concept
A single-winner election is a voting system where one candidate is chosen from a pool of candidates to hold a particular position, based on the majority or plurality of votes. This system is widely used in various democratic processes, emphasizing the importance of each vote in determining the outcome.
3