Definition: Euclidian Distance between x and y:
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d(x, y) = ||x - y||
Definition: Let S⊆ℝⁿ. A point a∈ℝⁿ is an interior point if:
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∃ε>0 s.t. B(a, ε)⊆S
Proposition: Let S⊆ℝⁿ and T = ℝⁿ\S. S is open if and only if
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T is closed
Definition: Given f:X→ℝ and x*∈X. x* is a global maximiser of f iff:
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∀x∈X: f(x)≤f(x*)
Theorem: If f is differentiable on an interval f is:
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continuous on that interval
Definition: Let S⊆ℝⁿ. A point a∈ℝⁿ is an accumulation (limit) point if:
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∀ε>0: B(a, ε)∩S≠∅
Definition: Let f:ℝⁿ→ℝ be continuous and a∈R. Then {x∈ℝⁿ | f(x)≤a} is:
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d(x, y) = ||x - y||
Definition: Let S⊆ℝⁿ. A point a∈ℝⁿ is an interior point if:
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∃ε>0 s.t. B(a, ε)⊆S
Proposition: Let S⊆ℝⁿ and T = ℝⁿ\S. S is open if and only if
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T is closed
Definition: Given f:X→ℝ and x*∈X. x* is a global maximiser of f iff:
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∀x∈X: f(x)≤f(x*)
Theorem: If f is differentiable on an interval f is:
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continuous on that interval
Definition: Let S⊆ℝⁿ. A point a∈ℝⁿ is an accumulation (limit) point if:
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∀ε>0: B(a, ε)∩S≠∅
Definition: Let f:ℝⁿ→ℝ be continuous and a∈R. Then {x∈ℝⁿ | f(x)≤a} is:
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