Math Problem of the Week Forum

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Undergrad Sum of an Alternating Series
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Undergrad What Is the Infimum of This Set of Superior Limits?
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3
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Undergrad Cohomology Ring of Complement of Hyperplanes in Complex n-space
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0
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Undergrad Find the Dimension of a Subspace of Matrices
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2
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Undergrad Fourier Series on the Unit Interval
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5
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Undergrad Limit of a Nonnegative Continuous Function
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1
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Undergrad A Function in the Continuous Hölder Class
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1
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Undergrad Does the Taylor series for arctan converge at x = 1?
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19
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Undergrad Groups of Prime Power Order
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1
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Undergrad Closed subspace of square-integrable functions on D
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13
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Undergrad Ext Functor on Noetherian Affine Schemes
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2
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Undergrad Flat Modules and Intersection
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2
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Undergrad First Cohomology of a Subscheme of Projective Plane
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2
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Undergrad Inequality of Determinants
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10
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Undergrad Is the Finite Expectation of Powers Satisfied by Nonnegative Random Variables?
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4
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Undergrad A Series Converging to a Lipschitz Function
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1
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Undergrad Neumann Boundary Value Problem in a Half Plane
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1
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Undergrad Positive Definite Block Matrices
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1
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Undergrad Projection Formula for Ringed Spaces
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1
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Undergrad Does the Alternating Binomial Sum Formula Hold for All Positive Integers?
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1
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Undergrad Integration Over a Line in the Complex Plane
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8
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Undergrad Estimate of a Principal Value Integral
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2
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Undergrad Positive Definiteness Determined from Symmetrized Products
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1
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Can You Solve This Advanced Definite Integral Using Residue Theorem?
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1
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Undergrad Power Sums Limits: Evaluating $\lim_{n\to \infty}$
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3
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Undergrad Boundedness of Oscillatory Integrals
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2
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Undergrad Solution to a Matrix Quadratic Equation
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4
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Undergrad A Nonlinear Elliptic PDE on a Bounded Domain
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3
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Undergrad Hölder Continuous Maps from ##R## to a Metric Space
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3
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Undergrad Attaching a Two-Cell to a Circle
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1
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Undergrad Weak Topology on an Infinite-Dimensional Hilbert Space
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1
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Undergrad Find Limit of $$\frac{x}{e} - \left(\frac{x}{x+1}\right)^x$$ at Infinity
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3
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Undergrad An Integral with Fractional Part
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3
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Undergrad Product of Two Finite Cyclic Groups
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1
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Undergrad Prove Hermitian Matrices Satisfy ##H^2 = H^\dagger H##
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22
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Undergrad Comparing Rank and Trace of a Matrix
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1
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Undergrad Local Integrability of a Maximal Function
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1
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Undergrad A Test for Absolute Convergence of a Series
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1
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Undergrad Analytic Functions with Isolated Zeros of Order k
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2
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Undergrad A Linear Operator with Trace Condition
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1
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Undergrad Steenrod Squares over an Infinite Projective Space
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1
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Undergrad Local Property of Flasque Sheaves
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2
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Undergrad Ramanujan Sums: Showing $c_n(k)$
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3
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Undergrad Translation-Invariant Operators on Lebesgue Spaces
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4
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Undergrad Definite Integral of a Rational Function
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6
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Undergrad Solve Linear System of ODEs: x',y' w/ Initial Conditions x(0),y(0)
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10
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Undergrad Smooth proper self-maps on Rn
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1
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Undergrad Preservation of Local Compactness
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4
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High School Inequality of Positive Real Numbers: Proving (1-1/x^2)(1-1/y^2)≥9 with x+y≤1
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12
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Undergrad Limit of Complex Sums: Find $$\lim_{n\to \infty}$$
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1
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Undergrad Is the Rank of AB Related to the Ranks of A and B?
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2
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Undergrad What is the Relationship Between Fiber Bundles of Spheres?
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1
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Undergrad Convergence of Random Variables in L1
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3
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Undergrad Orthonormal Bases on Hilbert Spaces
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7
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Undergrad Show That the Curve is Straight
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4
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Undergrad Gaussian Integrals in Two Dimensions
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3
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Undergrad Uniformly Continuous Functions on the Real Line
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15
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Undergrad Semisimple Tensor Product of Fields
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1
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Undergrad Sufficient Conditions for a Covering Space
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1
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Undergrad Exponential-Type Integrals
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11
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High School Integer n: Solving the Equation ##\dfrac{n^2+3}{2n+4}## for Integers
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14
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High School Solve 3-Variable Equation with Real Solutions | √(z-y^2-6x-26)+x^2+6y+z-8=0
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3
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Undergrad Expected Value of a Maximum
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14
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Undergrad Minimizers of an Energy Functional
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1
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Undergrad Contour Integral Representation of a Function
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4
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Undergrad Support of a Finitely Generated Module
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7
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High School How Can You Minimize This Complex Square Root Expression for Positive x and y?
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6
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Undergrad Infinite Sequences of Sines
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2
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44
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High School Prove that the roots of a polynomial cannot be all real
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5
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High School Can x(x+y) Be Proved to Be ≤ 2 for Positive Real Numbers?
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11
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High School Proving Inequality between Positive Real Numbers a and b: a(a+b) ≤ 2
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6
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High School Maximize (x1+x2)(x1+x3)x4 for Quartic Equation with Real Roots in [1/2,2]
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2
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Undergrad What is the Log Concavity of Determinants for Positive Definite Matrices?
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6
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Undergrad Convergence in Probability
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1
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High School Find Triplets of Positive Integers with Sum of Cubes
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3
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High School Can You Verify This Trigonometric Identity Involving Cosecant Functions?
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1
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Undergrad A Modified Basis in an Inner Product Space
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2
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High School What Is the Minimum Value of (a²+b²)/c² in Triangle ABC?
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1
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Undergrad Is Every Convex Function Differentiable at Most Points?
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2
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High School Find the Sum of Two Real Numbers | Solve a + b with Given Equations
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19
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High School Is the product of two radical expressions equal to six?
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13
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Undergrad In a Category with Fibered Products
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5
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High School Finding the Product of Real Roots: POTW Equation Solution
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9
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Undergrad Proof of Asymptotic Equality: $\sum_{n=0}^\infty a_n\frac{x^n}{n!} \sim ae^x$
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1
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Undergrad Problem of the Week #301 - June 28, 2022
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1
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High School What Is the Maximum Value of \( x \) in the Equation \( 2x+y+\frac{4}{xy}=10 \)?
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7
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Undergrad Can a Topological Space Be Homotopy Equivalent to a Cylinder?
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3
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High School What Is the Minimum Cosine Value in Trigonometric Constraints?
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2
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High School How Can We Find All Integer Pairs (k, n) That Satisfy This Factorial Equation?
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4
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High School What is the minimum value of a+b+c+d if a^2-b^2+cd^2=2022?
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5
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High School Minimum Value of (a+7)^2+(b+2)^2 with Constraint (a-5)^2+(b-7)^2=4 - POTW #506
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5
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High School Minimum Sum of Non-Negative Integers with Given Equation - POTW #504
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1
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Undergrad Is $SO(3)$ Path-Connected?
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1
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Undergrad Are There a Finite Number of Solutions to $f(x) = y$ in a Bounded Region?
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1
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Undergrad Projection Map $X \times Y$: Closure Property
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1
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Undergrad Can Continuity Ensure Infinite Limits in Nested Functions?
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1
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High School Can $\sin^5 x + \cos^3 x$ Equal 1?
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1
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High School Can This Infinite Product Surpass 50?
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1
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High School Can This Triangle Configuration Prove a Right Angle?
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1
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High School Can You Prove the Polynomial Has Three Distinct Roots?
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1
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