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4 Cards in this Set
- Front
- Back
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Cauchy Sequence |
A sequence X=(x_n) of real numbers is said to be Cauchy sequence if for every E>0 there exists a natural number H(E) such that for all numbers n,m>=H(E), the terms x_n,x_m satisfy |x_n-x_m|<E |
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Cluster Point |
Let A be a subset of R. A point c in R is a cluster point of A if for every d>0 there exists at least one point in x in A, which is not c, such that |x-c|<d |
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Limit |
Suppose f:A->R, suppose c is a cluster point of A. Suppose L is in R. Then lim_{x->c}f(x)=L means for every E>0, there exists d=d(E) such that if o<|x-c|<d and x is in A then |f(x)-L|<E |
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Continuous |
Suppose f:A->R, c is in A. f is continuous at c. Given E>0, there exists d=d(E) such that if |x-c|<d and x is in A, then |f(x)-f(c)|<E |
