👉 Mathematics is the study of numbers, quantities, shapes, and structures, using logic and reasoning to understand and describe these concepts. It encompasses a wide range of disciplines, from basic arithmetic and algebra to advanced calculus and topology. Key terms include:
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Number
: A quantity that can be counted or measured, including integers (like 1, 2, 3), fractions (like 1/2), decimals (like 0.5), and irrational numbers (like π or √2).
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Operation
: A process that combines or transforms numbers, such as addition (+), subtraction (-), multiplication (×), and division (÷).
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Function
: A relation between a set of inputs (domain) and a set of possible outputs (range), often represented by an equation or graph.
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Variable
: A symbol used to represent a quantity that can change, such as x or y.
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Equation
: A statement that two expressions are equal, like \( ax + b = c \).
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Variable
: Used to denote unknown values in equations and expressions.
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Limit
: A concept in calculus that describes the behavior of a function as the input values approach a specific point.
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Derivative
: A measure of how a function changes as its input changes, crucial in understanding rates of change and slopes.
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Integral
: The reverse operation of differentiation, used to find the area under curves or accumulate quantities.
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Set
: A collection of distinct objects, either finite or infinite, considered as a single entity.
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Proof
: A logical argument demonstrating the truth of a mathematical statement, often structured with premises leading to a conclusion.
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Algebra
: The study of symbols and the rules for manipulating them to solve equations and understand relationships between variables.
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Geometry
: The branch of mathematics dealing with shapes, sizes, positions, and dimensions of objects.
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Trigonometry
: A branch focusing on the relationships between the sides and angles of triangles, particularly useful in navigation and physics.
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Statistics
: The science of collecting, organizing, analyzing, interpreting, and presenting data.
These terms form the foundation of mathematical discourse, enabling precise communication and rigorous exploration of mathematical ideas.