Real Analysis function Question 8 Is every lesstinuous funct

Real Analysis (function)

Question 8

Is every lesstinuous function continuous? Is every continuous function lesstinuous? Explain. Decide if the following claims are true or false, providing either a short proof or counterexample to justify each conclusion. Assume throughout that g is defined and continuous on all of R. If g(x) > 0 for all x 0 as well. If g(r) = 0 for all r G Q, then g[x) = 0 for all x G R. If g(x_0) > 0 for a single point x_0 R, then g(x) is in fact strictly positive for uncountable many points.

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