ASL STEM

Inductive Set Sign Video

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Definition

A set of real numbers is called an inductive set if it has the following two properties: a) The number 1 is in the set. b) For every x in the set, the number x+1 is also in the set.

Source: Mathematical Analysis, second edition by Tom M. Apostol

Example

The set of all real numbers is an inductive set, as well as the set of all positive real numbers. The set of all positive integers is the smallest inductive set.

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> Mathematics

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> Inductive Set

+ Triangle Inequality *

+ Field Axioms *

+ Order Axioms *

- Inductive Set *

+ Euclid's Lemma *

+ Completeness Axiom *

+ Approximation Property *

+ Archimedean Property *

+ Cauchy Schwarz Inequality *

+ Stereographic Projection *

+ Imaginary Unit *

+ Principal Argument *

+ Peano's Axioms *

+ Interior Point *

+ Component Interval *

+ Adherent Point *

+ Accumulation Point *

+ Derived Set *

+ Cantor Intersection Theorem *

+ Bounded Set *

+ Metric Space *

+ Square Metric *

+ Heine Borel Covering Theorem *

+ Compact Set *

+ Lindelof Covering Theorem *

+ Fixed Point Theorem *

+ Euclidean Metric *

+ Cauchy Condition *

+ Fixed Point *

+ Inverse Image *

+ Bolzano's Theorem *

+ Disconnectedness *

+ Arcwise Connectedness *

+ Bounded (Function)

+ Heine's Theorem *

+ Discontinuity *

+ Differentiable

+ Removable Discontinuity *

+ Jump Discontinuity *

+ Monotonic Function *

+ Rolle's Theorem *

+ Cauchy's Mean Value Theorem *

+ Taylor's Theorem *

+ Partial Derivatives *

+ Cauchy Riemann Equations *

+ Bounded Variation *

+ Measure Zero *

+ Total Variation *

+ Rectifiable Curve *

+ Non Rectifiable Curve *

+ Geometric Series *

+ Riemann Stieltjes Integral *

+ Integration By Parts *

+ Step Function *

+ Euler's Summation Formula *

+ Riemann's Condition *

+ Oscillation *

+ Orientation Reversing *

+ Limit Superior *

+ Limit Inferior *

+ Telescoping Series *

+ Comparison Test *

+ Limit Comparison Test *

+ Dirichlet's Test *

+ Abel's Test *

+ Little Oh Notation *

+ Rearrangement *

+ Double Sequence *

+ Double Series *

+ Mertens' Theorem *

+ Dirichlet Product *

+ Cesaro Summability *

+ Infinite Product *

+ Uniform Boundedness *

+ Uniform Bound *

+ Almost Everywhere *

+ Weierstrass M Test *

+ Space Filling Curve *

+ Pointwise Convergence *

+ Bounded Convergence *

+ Big Oh Notation *

+ Mean Convergence *

+ Disk Of Convergence *

+ Series Expansion *

+ Taylor Series *

+ Binomial Coefficient *

+ Upper Function *

+ Lebesgue Integrable *

+ Interval Of Convergence *

+ Binomial Series *

+ Improper Riemann Integrable *

+ Cauchy Principle Value *

+ Orientation Preserving *

+ Continuously Differentiable *

+ Zeta Function *

+ Riemann Zeta Function *

+ Measurable Functions *

+ Characteristic Function *

+ Lebesgue Mesasure *

+ Gamma Function *

+ Dirichlet Integral *

+ Semimetric Space *

+ Riesz Fischer Theorem *

+ Fourier Series *

+ Square Integrable *

+ Orthogonal System *

+ Orthonormal System *

+ Dirichlet's Kernel *

+ Jordan's Test *

+ Fourier Integral Theorem *

+ Dini's Test *

+ Directional Derivative *

+ Integral Transform *

+ Riemann's Localization Theorem *

+ Total Derivative *

+ Gradient Vector *

+ Stationary Point *

+ Riemann Integrable *

+ Lagrange Multiplier *

+ Multiple Integral *

+ Triple Integral *

+ Saddle Point *

+ Functional Equation *

+ Quadratic Form *

+ Coordinate Transformation *

+ Contour Integral *

+ Jacobian Matrix *

+ Jacobian Determinant *

+ Double Integral *

+ Fubini's Theorem *

+ Beta Function *

+ Convolution *

+ Jordan Measure *

+ Open Mapping Theorem *

+ Inner Product *

+ Jordan Curve *

+ Piecewise Smooth *

+ Positively Oriented Circle *

+ Linear Homotopy *

+ Negatively Oriented Circle *

+ Liouville's Theorem *

+ Maximum Modulus Principle *

+ Minimum Modulus Principle *

+ Laurent Series *

+ Deleted Neighborhood *

+ Isolated Singularity *

+ Removable Singularity *

+ Gaussian Sum *

+ Conformal Mapping *

+ Mobius Transformation *

+ Essential Singularity *

+ Simple Pole *

+ Radius Of Convergence *

+ Complex Residue *

+ Monotonic Sequence *

+ Integral Test *

+ Implicit Function Theorem *

+ Bolzano Weierstrass Theorem

+ Mean Value Theorem

+ Cauchy Product *

+ Irremovable Discontinuity *

+ Complex Number *

+ Analytic Function *

+ Abel's Limit Theorem *

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