The discussion revolves around the existence of a bijection from set A to set X, given that B is a subset of X and there exists a bijection from A to B. The subject area involves concepts of set theory and cardinality.
The discussion is active, with participants offering differing perspectives on the conditions under which a bijection may or may not exist. Some suggest clarifying the relationship between B and X, while others propose examples to illustrate their points. There is no explicit consensus, but various interpretations and considerations are being explored.
There is mention of the need to specify whether B is a proper subset of X. Additionally, the discussion touches on the cardinality of sets, particularly in the context of finite and infinite sets, and the implications of these properties on the existence of bijections.
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##).UltrafastPED said:I asked a question; I did not provide an answer.
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.