Recent content by angelpsymon

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    Proving Existence of Fixed Points in Continuous Sets

    Alright, I think that I got it now. Thanks a lot guys.
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    Proving Existence of Fixed Points in Continuous Sets

    Homework Statement Suppose f:[a,b] \rightarrow [a,b] is continuous. Prove that there is at least one fixed point in [a,b] - that is, x such that f(x) = x. Homework Equations The Attempt at a Solution I was going to try something with the IVT, but then I realized I wasn't sure what...
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    Proving f(x) has a limit at all points not odd

    yes, it is the floor symbol, the others are delta and epsilon
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    Proving f(x) has a limit at all points not odd

    1. Define f:R→R as follows: f(x)= x- ⌊x⌋ if ⌊x⌋ is even. f(x)= x- ⌊x+1⌋ if ⌊x⌋ is odd. Determine those points where f has a limit and justify your conclusions (using δ and ε). Homework Equations 3. The attempt at a solution involved a graph of the situations of f(x)...