Recent content by mizunoami

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    Equal sets and bijective correspondence

    I mean equal - so both sets contain the same elements. Yeah, there is obviously a bijection. But how can I show that using a rigorous mathematical proof?
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    Open set is a collection of regions

    This TOTALLY makes my day. WOOHOO! THANKS :)
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    Equal sets and bijective correspondence

    Homework Statement If [n] and [m] are equal, then they are bijective correspondent. I define f \subset\{(n,m)\mid n \in [n], m\in [m]\}. Suppose [n]=[m]. Let(n,m_1),(n,m_2)\in f. Because [n]=[m], then m_1=m_2. So for all n \in [n], there exists a unique m\in [m] such that f(n)=m. So f...
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    Open set is a collection of regions

    Yeah. Then why is U a subset of the union of regions? Since I'm showing U=union of regions, I want to show that U is a subset of the union of regions, and the union of regions is the subset of U. Thanks a lot!
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    Open set is a collection of regions

    If a,b \in C and a<b, then the set of points between a and b is the region ab. Thanks!
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    Open set is a collection of regions

    Can someone please help? A new proof is good too. Thanks!
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    Open set is a collection of regions

    Homework Statement Let U be a nonempty open set. The U is the union of a collection of regions. 2. The attempt at a solution Let x be an element of U. There exists a region R such that x is in R and R is in U. So x is also in the union of a collection of regions Rx. Then U is a...