# Analysis Countinuity Problem

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• Nov 11th 2006, 11:07 AM
JackStolerman
Analysis Countinuity Problem
Was wondering if someone could outline the following problem:

Let g: R to R by defining g(x) as 2x for x rational and as x+3 for x irrational. Find all the points where g is continuous and prove your assertion.

Thanks for any help.
Jack
• Nov 11th 2006, 11:54 AM
Plato
Do you know how to solve 2x=x+3?
• Nov 11th 2006, 01:15 PM
JackStolerman
Well how would I prove the assertion?
• Nov 11th 2006, 01:34 PM
Plato
Well prove that it is continuous only at 3.
• Nov 11th 2006, 01:47 PM
ThePerfectHacker
Basically the Dirchelet function.

When we approach a number (limit at the point) by rationals we get one value and when we approach a number (limit at the point) by irrationals we might get a different value. Well, approaching a number (limit) by rationals is anagolous with the irrationals because the irrationals are contrsucted by a Cauchy sequence of rationals. Thus, what Plato said is to solve the equation, for it says the rationals and irrationals produce the same limit (which must be if it exists).