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In the Wolfram Language, Piecewise expressions default to 0 wherever your arguments to the function don't define them. This makes them defined for all real numbers which is mostly convienent for programming. Piecewise[{{8 - 3*t, 1
Before attempting the cuts, how would you visualize the set of rationals itself, in such a way that you distinguish it from the set of reals? It is an interesting problem.
I learned something from your posting. Thank you. I thought from previous experiments that WolframAlpha didn't understand assignments to variables. Perhaps I was wrong or perhaps this is something new that has been added. If it is new then I wonder...