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Mathematical Symbols and Notation

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xnx^n

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Exponential notation, where nn is the exponent and xx is the base, representing xx multiplied by itself nn times.

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==

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Equality symbol that denotes that two expressions are equal in value.

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\sum

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Summation symbol used to denote the sum of a series of terms.

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\nabla

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Del operator used in vector calculus, often to denote the gradient, divergence, or curl of a field.

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\infty

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Infinity symbol that represents an unbounded limit or quantity that is larger than any real number.

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\exists

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Existential quantification symbol meaning 'there exists' or 'there is at least one'.

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ii

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Imaginary unit, used in complex numbers, where i2=1i^2 = -1.

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\forall

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Universal quantification symbol meaning 'for all' or 'for every'.

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\neq

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Inequality symbol that denotes that two expressions are not equal in value.

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\approx

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Approximation symbol used when two values are close in value but not exactly equal.

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\bigcup

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Union symbol in set theory denoting the set containing all elements from the given sets.

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\bigcap

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Intersection symbol in set theory indicating the set of elements common to all given sets.

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logb(x)\log_b (x)

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Logarithm of xx to the base bb, representing the exponent to which bb must be raised to produce xx.

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×\times

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Multiplication symbol that denotes the product of two values.

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π\pi

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Pi, a mathematical constant representing the ratio of a circle's circumference to its diameter.

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<<

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Less than symbol used to compare two values, where the first is smaller than the second.

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x\sqrt{x}

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Square root symbol, denoting a number that, when multiplied by itself, gives the number xx.

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>>

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Greater than symbol used to compare two values, where the first is larger than the second.

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ab\frac{a}{b}

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Fraction notation, with aa being the numerator and bb being the denominator, representing the division of aa by bb.

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\geq

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Greater than or equal to symbol, indicating that the first value is either greater than or equal to the second.

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\int

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Integral symbol, fundamental concept in calculus used to find areas under curves and accumulation of quantities.

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limxaf(x)\lim_{x \to a} f(x)

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Limit notation, expressing the value that function f(x)f(x) approaches as xx approaches aa.

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\partial

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Partial derivative symbol used to indicate a derivative with respect to one variable while holding others constant.

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\emptyset

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Empty set symbol representing a set that contains no elements.

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÷\div

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Division symbol representing the division of one quantity by another.

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\leq

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Less than or equal to symbol, indicating that the first value is either less than or equal to the second value.

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Δ\Delta

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Delta, commonly used to denote change or difference in a quantity.

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++

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Addition symbol used to indicate the sum of two numbers or expressions.

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-

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Subtraction symbol used to represent the difference between two numbers or expressions.

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θ\theta

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Theta, often used to represent an angle in geometry and trigonometry.

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