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Advanced Mathematical Terms
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Hint (not exact definition)
Answer
a vector having length 1
a set for which there exists a bijection of the natural numbers onto the set itself
a special limit often calculated to find the area under a curve
the dimension of the column space of a matrix
a sequence that is either increasing or decreasing
coordinate system that simplifies the evaulation of integrals over regions bounded by spheres or cones, for example
another word for the scalar product of two vectors
a set in a metric space is called this if its complement is open
the algebraic property which states that for any two real numbers a and b, a + b = b + a
the sum of any scalar multiples of vectors
a function that is both injective and surjective
a type of integral where either the integrand or interval of integration is unbounded
the set of all subsets of a set
a prime number that differs from another prime number by two
for two random variables, this is equal to their covariance divided by the product of their standard deviations
a sequence which is defined by preceding terms in the sequence and an initial condition
Hint (not exact definition)
Answer
if the derivative of a function is increasing or decreasing on an interval, the graph will have this property on that interval
two vectors are said to be this if their dot product is zero
another name for a number which satisfies the conditions for being the least upper bound of a set
used for finding the derivative of compositions of functions
a square matrix is invertible if and only if its ________ is not zero
a set and an operation which can is used to combine two elements of the set to produce a third element
for two sets A and B, the set of all elements x such that x is in A and x is in B
the name for a point of a function where the derivative is 0 or is not defined
property of a metric space where every Cauchy sequence in the space converges to a point in the space
a more formal term for a one to one function
an n x n matrix A is said to have this property if there exists an n x n matrix C such that AC = I and CA = I, where I is the n x n identity matrix.
an operation that finds the remainder after division between two numbers
a special limit often calculated to find the equation of the slope of a tangent line
two vectors are said to be this if they are scalar multiples of each other
usually used to prove statements about natural numbers, consists of a basis step and an inductive step
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