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#1 2007-09-15 12:58:09
- fusilli_jerry89
- Member
- Registered: 2006-06-23
- Posts: 86
Rational and Irrational Limits
Let f(x) = { x² if x is rational
{ 0 if x is irrational
Prove that lim f(x) = 0
x->0
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#2 2007-09-16 01:48:48
- mathsyperson
- Moderator
- Registered: 2005-06-22
- Posts: 4,900
Re: Rational and Irrational Limits
Why did the vector cross the road?
It wanted to be normal.
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#3 2007-09-16 08:57:32
- HallsofIvy
- Guest
Re: Rational and Irrational Limits
Given epsilon> 0, take delta = sqrt(epsilon). If |x- 0|= |x|< delta, then either
1. x is rational, in which case |f(x)- 0|= |x^2- 0|< delta^2= epsilon
2. x is irrational, in which case |f(x)-0|= |0- 0|< epsilon.
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