Let A = {r belongs to Q : e < r < pi} show that A...

Let A = {r belongs to Q : e < r < pi} show that A is closed and bounded but not compact

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Colby Messinger answered 2 years ago

Let E = Q(√a), where a is an integer that is not a perfect square. Show...

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It is known that the sentence E: if (if P then not (Q or R) else...

It is known that the sentence E: if (if P then not (Q or R) else not P) then (not (Q and S) if and only if (not Q or not S)). Investigate whether I = {S ← false, R ← false, Q '← true, P ← false} interpretations are interpretations for sentence E.

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(a) Let <X, d> be a metric space and E ⊆ X. Show that E is connected iff for all p, q ∈ E, there is a connected A ⊆ E with p, q ∈ E. b) Prove that every line segment between two points in R^k is connected, that is Ep,q = {tp + (1 − t)q | t ∈ [0, 1]} for any p not equal to q in R^k. C). Prove that every convex subset of R^k...

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Let A = {r belongs to Q : e < r < pi} show that A...

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