1. Let a < b. (a) Show that R[a, b] is uncountable

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Colby Messinger answered 2 years ago

Let R=R+. Define: a+b = ab ; ab = a^(lnb) 1. Is (R+, +, ) a...

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Let f : [a, b] → R be a monotone function. Show that the discontinuity set Disc(f) is countable.

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Let L be the set of all languages over alphabet {0}. Show that L is uncountable, using a proof by diagonalization.

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5. (a) Let f : R \ {−1} → R, f(x) = x+1. Show that f...

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1.- Show that (R, τs) is connected. Also show that (a, b) is connected, with the...

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(V) Let A ⊆ R, B ⊆ R, A 6= ∅, B 6= ∅ be two...

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