Question

Prove : If S is an infinite set then it has a subset A which is...

Prove : If S is an infinite set then it has a subset A which is not equal to S, but such that A ∼ S.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Prove that a subset of a countably infinite set is finite or countably infinite.
Prove that a subset of a countably infinite set is finite or countably infinite.
Suppose that E is a closed connected infinite subset of a metric space X. Prove that...
Suppose that E is a closed connected infinite subset of a metric space X. Prove that E is a perfect set.
Use the definition to prove that any denumerable set is equinumerous with a proper subset of...
Use the definition to prove that any denumerable set is equinumerous with a proper subset of itself. (This section is about infinite sets)
Prove Cantor’s original result: for any nonempty set (whether finite or infinite), the cardinality of S...
Prove Cantor’s original result: for any nonempty set (whether finite or infinite), the cardinality of S is strictly less than that of its power set 2S . First show that there is a one-to-one (but not necessarily onto) map g from S to its power set. Next assume that there is a one-to-one and onto function f and show that this assumption leads to a contradiction by defining a new subset of S that cannot possibly be the image of...
[Q] Prove or disprove: a)every subset of an uncountable set is countable. b)every subset of a...
[Q] Prove or disprove: a)every subset of an uncountable set is countable. b)every subset of a countable set is countable. c)every superset of a countable set is countable.
Prove that the set of odd numbers is infinite.
Prove that the set of odd numbers is infinite.
Prove that if a subset of a set of vectors is linearly dependent, then the entire...
Prove that if a subset of a set of vectors is linearly dependent, then the entire set is linearly dependent.
41. Prove that a proper subset of a countable set is countable
41. Prove that a proper subset of a countable set is countable
Show that every infinite semi-decidable language A has an infinite subset B⊆A such that B is...
Show that every infinite semi-decidable language A has an infinite subset B⊆A such that B is a decidable language.
For a nonempty subset S of a vector space V , define span(S) as the set...
For a nonempty subset S of a vector space V , define span(S) as the set of all linear combinations of vectors in S. (a) Prove that span(S) is a subspace of V . (b) Prove that span(S) is the intersection of all subspaces that contain S, and con- clude that span(S) is the smallest subspace containing S. Hint: let W be the intersection of all subspaces containing S and show W = span(S). (c) What is the smallest subspace...