- #1

aaaa202

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be a bijection. If B is a subset of X. Can there still exist a bijection from A to X?

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- Thread starter aaaa202
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- #1

aaaa202

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be a bijection. If B is a subset of X. Can there still exist a bijection from A to X?

- #2

UltrafastPED

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But A is already fully mapped onto B, so which elements of A are left to map onto the X - B?

- #3

aaaa202

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So there exists a bijection between each of these sets even though, the even natural numbers are a subset of the natural numbers. So I think you're actually wrong?

- #4

UltrafastPED

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However it seems that you now know the answer: I think you are saying "for finite sets the answer is NO; for infinite sets the answer is YES". Next you should go ahead and construct an example using the set of natural numbers and subsets of odds and evens.

- #5

HallsofIvy

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You might want to re-write the question to specify that B is a **proper** subset of X.

- #6

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It should be mentioned that it isn't always true for infinite sets. E.g., take ##A = B = \mathbb{R}## and ##X = \mathbb{Z}##. In general it will be possible only if ##X## has the same cardinality as ##B## (and hence the same cardinality as ##A##).

However it seems that you now know the answer: I think you are saying "for finite sets the answer is NO; for infinite sets the answer is YES". Next you should go ahead and construct an example using the set of natural numbers and subsets of odds and evens.

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