Interactive Real Analysis
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Real Analysis
1. Sets and Relations
2. Infinity and Induction
3. Sequences of Numbers
4. Series of Numbers
5. Topology
6. Limits, Continuity, and Differentiation
6.1. Limits
6.2. Continuous Functions
6.3. Discontinuous Functions
6.4. Topology and Continuity
6.5. Differentiable Functions
6.6. A Function Primer
7. The Integral
8. Sequences of Functions
9. Historical Tidbits
Java Tools
6.1. Limits
Proposition 6.1.9: Limits and OneSided Limits
f(x) = L
if and only if
f(x) = L
and
f(x) = L
Context
Proof:
The proof of this basically a rewriting of the definitions involved. It is left as an exercise.
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