Digging Deeper into the Real Numbers

Real analysis studies the properties of real numbers, sequences, and functions. It lays the groundwork for understanding limits, continuity, and convergence.

Core Concepts

• Limits: Describes the behavior of a function as it approaches a certain point.
• Continuity: Ensures functions behave smoothly without sudden jumps.
• Sequences and Series: Explore how numbers can approach a value (converge) or not (diverge).

Real-World Relevance

Real analysis is crucial in engineering, economics, and computer science, especially when precision and rigor are needed.

Explore Further

• Investigate whether a sequence like \(a_n = 1/n\) converges.
• Examine if the function \(f(x) = 1/x\) is continuous at \(x = 0\).