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The following general topics can be used to guide your more specific topic selection: Explain the process of constructing the real number system beginning with
The following general topics can be used to guide your more specific topic selection:
- Explain the process of constructing the real number system beginning with the natural numbers.
- Prove implications of axioms and properties of the real number system.
- Describe the concept of an ordered field as it applies to the real number system.
- Describe the idea of a limit of a function at a point.
- Determine whether a given function is continuous, discontinuous, or uniformly continuous.
- Explain the connection between the continuity of a function at a point and the function being differentiable at a point.
- Prove and apply the fundamental theorem of calculus in finding the value of specific Riemann integrals of functions.
- Document the proof in detail with comprehensive supporting information, specifically:
- Ensure mathematical representations (equations, diagrams, graphs, etc.) are clear and appropriate.
- Ensure that your use of mathematical terminology and notation is accurate.
- Present all of the main elements of the mathematical proof, including axioms and theorems.
- Explain the significant mathematical concepts involved in your proof.
- Provide a thorough oral defense, speaking clearly and effectively.
- Organize your presentation in a logical way and pace the transitions so that the material is easily accessible to your audience of peers.
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