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votes
1answer
15 views

Clarify Cartesian Products and Binary Operations

So tell me if I'm saying this write. A Cartesian Product is a function f:X x Y --> Z , where some unknown structural operation on the sets X and Y produces a set Z as its codomain, and Z is a set of ...
1
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0answers
58 views

Zuckerman's “Sets and Transfinite Numbers”

I am beginning a study in set theory and I found an old book in my school's library by Martin Zuckeman called Sets and Transfinite Numbers which was published in the 1970's. Has anyone used this text ...
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1answer
26 views

Union of Dedekind-finite sets

$F$ is Dedekind-finite if for every $A\varsubsetneq F$ we have $A<_cF$. Need help to prove that if $F,G$ are Dedekind-finite sets, $F\cap G=\emptyset$ then $F\cup G$ is also Dedekind-finite. ...
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2answers
44 views

Image of a proper class under one-one function is a proper class

Working under Zermelo-Franenkel set theory. how I can prove following: Let $V$ be proper class. Let $F : V \rightarrow U$ be a one-one function. Then $U$ has to be a proper class.