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Investigating mathematics consists of

a problem

These are components of an investigation, not a sequence of steps to be followed. For example, often in the midst of analyzing a problem you realize that the problem statement needs more clarification or that you must make further assumptions. And critiquing can take place at any time. Very often an investigator working on a problem falls into an alternating sequence of analysis of the problem and critique of the analysis.

Here's a report of an investigation in which that alternation takes place.

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