question on continuity from an SNS exam
Let $f:mathbb{R} rightarrow mathbb{R} $ a function such that $f(x) = 0$ if $x$ is irrational while, if $x = frac{p}{q}$ with $(p,q) = 1; p,q in mathbb{Z}$, $f(x) = frac{1}{q}$. Where is $f(x)$continuos?
I don't know where to begin...
real-analysis
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Let $f:mathbb{R} rightarrow mathbb{R} $ a function such that $f(x) = 0$ if $x$ is irrational while, if $x = frac{p}{q}$ with $(p,q) = 1; p,q in mathbb{Z}$, $f(x) = frac{1}{q}$. Where is $f(x)$continuos?
I don't know where to begin...
real-analysis
2
This is known as the Tomae function and is popular in most analysis book and wikipedia as well. It's continuous at those irrationals.
– DeepSea
Nov 30 '18 at 19:48
add a comment |
Let $f:mathbb{R} rightarrow mathbb{R} $ a function such that $f(x) = 0$ if $x$ is irrational while, if $x = frac{p}{q}$ with $(p,q) = 1; p,q in mathbb{Z}$, $f(x) = frac{1}{q}$. Where is $f(x)$continuos?
I don't know where to begin...
real-analysis
Let $f:mathbb{R} rightarrow mathbb{R} $ a function such that $f(x) = 0$ if $x$ is irrational while, if $x = frac{p}{q}$ with $(p,q) = 1; p,q in mathbb{Z}$, $f(x) = frac{1}{q}$. Where is $f(x)$continuos?
I don't know where to begin...
real-analysis
real-analysis
asked Nov 30 '18 at 19:47
LanceLance
8912
8912
2
This is known as the Tomae function and is popular in most analysis book and wikipedia as well. It's continuous at those irrationals.
– DeepSea
Nov 30 '18 at 19:48
add a comment |
2
This is known as the Tomae function and is popular in most analysis book and wikipedia as well. It's continuous at those irrationals.
– DeepSea
Nov 30 '18 at 19:48
2
2
This is known as the Tomae function and is popular in most analysis book and wikipedia as well. It's continuous at those irrationals.
– DeepSea
Nov 30 '18 at 19:48
This is known as the Tomae function and is popular in most analysis book and wikipedia as well. It's continuous at those irrationals.
– DeepSea
Nov 30 '18 at 19:48
add a comment |
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2
This is known as the Tomae function and is popular in most analysis book and wikipedia as well. It's continuous at those irrationals.
– DeepSea
Nov 30 '18 at 19:48