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Proof by Contradiction
Last updated Nov 1, 2022
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A Nonempty Set is Compact in the Order Topology iff it is Tightly Bounded and Complete
A Set is a Basis iff it is a Maximal Linearly Independent Set
A Set is a Basis iff it is a Minimal Spanning Set
A finite measure is absolutely continuous wrt another iff small sets on the other measure are also small on it
Almost Sure Convergence does not imply Lp Convergence
Closure of a Set is all its Limit Points
Convergence of a Bounded Sequence is determined by Convergent Subsequences
Dimension of a Vector Space lower bounds Spanning Set size
Epsilon Principle
Every Connected Set is contained in a single Component
Finite Extremums get arbitrarily close
Fourier Expansion of a Pseudo-Boolean Function
Growing a Linearly Independent Set
House Rules and Conventions
Infinite Pigeonhole
Linearly Independent Set Size is Unbounded iff there exists an Infinite Linearly Independent Set
Net Limits are unique in Hausdorff Spaces
Satisfiable Theory
Sequence Limits are unique in Hausdorff Spaces
Interactive Graph