Understanding Counterexamples In Analysis Index

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  • The field of real numbers can be ordered and the field of complex numbers cannot be ordered. But how many distinct orders can ...
  • a discontinuous function of two variables that is continuous in each variable separately This example is from
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  • PHI210 Building Counterexamples by analysis
  • Real numbers form a complete ordered field, but can every field be ordered? We explain what is an ordered field, and we state the ...

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Is it possible for a function to be unbounded in some neighborhood of every point of its domain? We construct a function that is ...

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