Practice question · Fill in the blanks
Complete the description of mathematical structure.
Because every theorem is proven from what lies beneath it, mathematical knowledge is ______.
Word bank: circular · cumulative · experimental · provisional
Hints
- Each result rests on results already established.
- Two of these words would describe science rather than mathematics.
Show the answer
Because every theorem is proven from what lies beneath it, mathematical knowledge is cumulative.
Why
Mathematics is cumulative: results build permanently on established ones. It is deliberately not circular (that would be a fallacy), and unlike experimental science its established theorems are not provisional, a proven theorem stays proven.
Practise The Structure of Mathematical Reasoning
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