Category:Real Analysis

1

• UTLOC:1

2

• 2-Dimensional rotation matrix

A

• A monotonically increasing sequence bounded above converges
• Abs (function)
• Absolute value
• Absolute value (function)
• Absolute value (object)
• Algebra
• Algebra (disambiguation)
• Common integrals table
• Axiom of completeness
• Axiom of completeness/Statement

B

• Bernstein polynomial
• Bernstein polynomial/Definition
• Bounded sequence

C

• Cantor's construction of the real numbers
• Cantor's construction of the real numbers/Definition
• Cauchy criterion for convergence
• Cauchy sequence
• Cauchy sequence/Definition
• Cauchy sequence/Short definition
• Cauchy-Schwarz inequality
• Cauchy-Schwarz inequality for inner product spaces
• Class of smooth real-valued functions on R-n
• Class of smooth real-valued functions on R-n/Structure
• Classes of continuously differentiable functions
• Closure (topology)
• Comparison test for real series
• Comparison test for real series/Statement
• Completeness
• Continuity
• Convergence of a sequence
• Convergent (sequence)
• Convergent sequence
• Converges (sequence)

D

• Differentiability
• Differentiation (subject)

E

• Epigraph
• Epsilon form of inequalities
• Equivalence of Cauchy sequences
• Euclidean n-space
• Every convergent sequence is Cauchy
• Every lingering sequence has a convergent subsequence
• Every sequence in a compact space is a lingering sequence

F

• Floor (function)
• Floor function
• Fréchet derivative

G

• Gateaux derivative
• Geometric progression
• Geometric sequence
• Geometric series
• Given a Hilbert space and a non-empty, closed and convex subset then for each point in the space there is a closest point in the subset
• Graph
• Greater than or equal to
• Greater than or equal to/Epsilon form

I

• If a real series converges then its terms tend to zero
• If a subsequence of a Cauchy sequence converges then the Cauchy sequence itself also converges
• If an inner product is non-zero then both arguments are non-zero
• Infimum
• Integers
• Integral
• Intermediate value theorem

K

• Kronecker delta

L

• Limit
• Limit (sequence)
• Limit of increasing sequence of sets
• Line
• Lingering sequence

M

• Mean value theorem
• Notes:Mean value theorem

M cont.

• Metrics
• Min/max
• Minimum
• Minimum function
• Modulus operation
• Monotonic
• Monotonicity of the integral of non-negative extended-real-valued measurable functions with respect to a measure

O

• Open balls
• Operations on convergent sequences of real numbers

P

• Positive and negative parts of a function

R

• Real numbers
• Real sequence
• Real sequences

S

• Sequence
• Series
• Series (summation)
• Notes:Simple function approximation to a numerical function
• Square root
• Square root (real function)
• Strong derivative
• Sub-sequence
• Subsequence
• Subsequence/Definition

T

• The integers
• The norm of a space is a uniformly continuous map with respect to the topology it induces
• The real line
• The real numbers
• The zero-to-the-power-of-zero problem
• Totally bounded
• Triangle inequality

U

• Uniformly continuous
• Usual topology of the reals

W

• Weak derivative
• Weierstrass approximation theorem