👉 Mathematical clarity hinges on precise notation, logical structure, and avoiding ambiguity. For example, defining variables unambiguously (e.g., \( x \) as a real number) and using consistent notation (e.g., \( f(x) \) for function values) ensures readers interpret equations correctly. A clear proof follows a logical sequence: starting with hypotheses, applying axioms or theorems step-by-step, and concluding with a justified final statement. For instance, proving \( a + b = c \) involves defining operations, assuming premises (e.g., \( a+b=d \)), and using the definition of equality to derive \( c = d \). This structured approach eliminates confusion, making mathematical reasoning transparent and replicable.
