Monotone Subsequence Theorem
October 29, 2024
This is a proof of the Monotone Subsequence Theorem.
Read moreExplore Mathematics
Discover the beauty and power of mathematical concepts, from fundamental theories to advanced proofs. Explore the language that describes the patterns and structures of our world.
Theorems and Proofs
Ratio Test
October 28, 2024
This a proof of the Ratio Test for convergence of series.
Read moreConvergence of inverse of a null sequence
October 25, 2024
This is a proof that the inverse of a null sequence is not convergent.
Read moreProperty of the n-th Root of a Positive Convergent Sequence
October 24, 2024
This is a proof that the n-th root of a positive convergent sequence is also convergent.
Read moreClosure of a Set
October 21, 2024
The closure of a set is the union of the interior of the set and the boundary of the set.
Read moreField of Real Numbers
October 18, 2024
Proof the real numbers are a complete field.
Read moreA Construction of the Real Numbers
October 17, 2024
Constructing the real numbers using Cauchy sequences of rational numbers.
Read moreConvergent Sequence of Rational Numbers
October 16, 2024
This is as proof that a convergent sequence of rational numbers is a Cauchy sequence.
Read moreCircumference Equation from Complex Numbers
October 9, 2024
This is a derivation of the equation of a circumference from complex numbers.
Read moreLinear Combination of Null Sequences
October 7, 2024
This is a proof that the linear combination of null sequences is a null sequence.
Read moreExponential Form of Complex Numbers
October 2, 2024
This is a deduction of the exponential form of a complex number.
Read moreCountability of Algebraic Numbers
September 30, 2024
This is a proof that the set of algebraic numbers is countable.
Read moreCountability of Trascendental Numbers
September 30, 2024
This is a proof that the set of trascendental numbers is uncountable.
Read moreCountability of Real Numbers
September 27, 2024
This is as proof that real numbers are uncountable.
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