User:Keith.U

Undergraduate mathematics\statistics student. Areas of study: Real analysis, metric spaces, probability theory.

Pages I've Created or Refactored
This exists as a quick reference for me to check over previous pages I've created or done major edits on, so that I may keep track of what I've done and round out entries made while perhaps overtired. If a page you have created or done significant work on appears here, please don't take this to mean I'm trying to claim any credit for your work. Again, this is so I may easily check for any "proofread", "tidy" or "refactor" tags that might arise, so I may correct my mistakes.

Sum of Geometric Progression/Corollary 2

Defining Sequence of Natural Logarithm is Strictly Decreasing

Lower Bound of Natural Logarithm/Proof 3

Definition:Jump Discontinuity

Discontinuity of Monotonic Function is Jump Discontinuity

Surjective Monotone Function is Continuous

Upper Bound of Natural Logarithm/Proof 2

Logarithm is Increasing

Logarithm of Power/Natural Logarithm/Rational Power

Logarithm of Power/Natural Logarithm/Integer Power

Logarithm of Power/Natural Logarithm/Natural Power

Limit of Bounded Convergent Sequence is Bounded

Sum of Logarithms/Natural Logarithm/Proof 3

Logarithm of 1 is 0/Proof 3

Upper Bound of Natural Logarithm/Proof 2

Subsets Inherit Uniform Convergence

Exponential with Base Greater than One is Strictly Increasing/Real Number

Defining Sequence of Natural Logarithm is Convergent

Book:Charles C. Pugh/Real Mathematical Analysis/Second Edition

Definition:Pointwise Equicontinuous

Definition:Uniformly Equicontinuous

Uniformly Convergent iff Difference Under Supremum Norm Vanishes

Definition:Natural Logarithm/Positive Real/Definition 3

Exponential with Arbitrary Base is Continuous

Rational Sequence Increasing to Real Number

Rational Sequence Decreasing to Real Number

Definition:Less Than (Real Numbers)

Definition:Strictly Positive/Real Number/Definition 2

Exponent Combination Laws/Power of Power

Definition:Power (Algebra)

Inequality of Product of Unequal Numbers

Absolute Value Inequality is Compound Inequality/Corollary

Absolute Value Inequality is Compound Inequality

Exponent Combination Laws/Product of Powers

Exponent Combination Laws/Product of Powers/Proof 2/Lemma

Number Equal to Zero iff Arbitrarily Small

Pasting Lemma/Corollary 2

Pasting Lemma/Corollary 1

Pasting Lemma

Euler's Number to Rational Power Permits Unique Continuous Extension

Exponential with Rational Power Permits Unique Continuous Extension

Exponential Tends to One as Power Tends to Zero/Rational Number

Exponential with Base between Zero and One Tends to One as Power Tends to Zero/Rational Number

Exponential with Base Greater Than One Tends to One as Power Tends to Zero/Rational Number

Exponential with Base Greater Than One Tends to One as Power Tends to Zero/Rational Number/Lemma

Exponential is Monotonic/Rational Number

Taking Additive Inverses Reverses Inequality

Power of Positive Real Number is Positive/Natural Number

Power of Positive Real Number is Positive/Integer

Power of Positive Real Number is Positive/Rational Number

Inequality iff Difference is Positive

Exponential with Base Between Zero and One is Strictly Decreasing/Natural Number

Exponential with Base Greater than One is Strictly Increasing/Natural Number

Exponential with Base Between Zero and One is Strictly Decreasing/Integer

Exponential with Base Greater than One is Strictly Increasing/Integer

Exponential with Base Between Zero and One is Strictly Decreasing/Rational Number

Exponential with Base Greater than One is Strictly Increasing/Rational Number

Root of Reciprocal is Reciprocal of Root

Root is Strictly Increasing

Power Function is Strictly Increasing over Positive Reals/Natural Exponent

Real Number between Zero and One is Greater than Power/Natural Number

Power is Well-Defined/Rational

Power is Well-Defined/Integer

Exponential Function is Continuous/Real Numbers/Proof 4

Definition:Exponential/Real

Moore-Osgood Theorem

Logarithm is Strictly Increasing and Strictly Concave/Corollary

Euler's Number: Limit of Sequence implies Base of Logarithm

Exponential Sequence is Eventually Increasing

Derivative of Exponential Function/Complex

Product of Uniformly Convergent Sequences of Bounded Functions is Uniformly Convergent

Uniformly Convergent Sequence of Bounded Functions is Uniformly Bounded

Derivative of Sequence of Holomorphic Functions

Definition:Bounded Sequence/Complex/Unbounded

Definition:Bounded Sequence/Complex

Uniformly Convergent Sequence Evaluated on Convergent Sequence

Exponential Sequence is Uniformly Convergent on Compact Sets

Identity Theorem

Vitali's Convergence Theorem

Montel's Theorem

Definition:Locally Bounded

Definition:Locally Bounded/Family of Mappings

Definition:Uniformly Bounded

Definition:Locally Bounded/Mapping