Is a function that has finite side limits monotonous? Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Monotone increasing function has finite one-sided limits at every pointSet of discontinuities of a function that has both limits at each point of $R$Does a function with left limits have only countable jumps?Proving a bounded monotone function has finite one-sided limitsIf $f$ has both one-way limits on $[a,b]$ , then $f$ is boundedMonotonous function and setsShow that the subset of strictly monotonous functions in $C(I)$ is nowhere denseProve that $f'$ is continuous, knowing that it has lateral limitsShould every injective function be non monotonous?Is it true that if continuous $f(x)$ has a limit then $f(nx_0)$ has a limit for any $x_0$?
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Is a function that has finite side limits monotonous?
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Monotone increasing function has finite one-sided limits at every pointSet of discontinuities of a function that has both limits at each point of $R$Does a function with left limits have only countable jumps?Proving a bounded monotone function has finite one-sided limitsIf $f$ has both one-way limits on $[a,b]$ , then $f$ is boundedMonotonous function and setsShow that the subset of strictly monotonous functions in $C(I)$ is nowhere denseProve that $f'$ is continuous, knowing that it has lateral limitsShould every injective function be non monotonous?Is it true that if continuous $f(x)$ has a limit then $f(nx_0)$ has a limit for any $x_0$?
$begingroup$
Consider a function $f:mathbbR to mathbbR$ which has finite side limits at any real point. Is this function monotonous? I know that the converse is true, but I wonder if this also holds.
real-analysis functions
asked Mar 31 at 18:08
MathEnthusiastMathEnthusiast
47913
$endgroup$
add a comment |
$begingroup$
Consider a function $f:mathbbR to mathbbR$ which has finite side limits at any real point. Is this function monotonous? I know that the converse is true, but I wonder if this also holds.
real-analysis functions
asked Mar 31 at 18:08
MathEnthusiastMathEnthusiast
47913
$endgroup$
2
$begingroup$
Try with $x^2$.
$endgroup$
– Yves Daoust
Mar 31 at 18:16
add a comment |
$begingroup$
Consider a function $f:mathbbR to mathbbR$ which has finite side limits at any real point. Is this function monotonous? I know that the converse is true, but I wonder if this also holds.
real-analysis functions
asked Mar 31 at 18:08
MathEnthusiastMathEnthusiast
47913
$endgroup$
Consider a function $f:mathbbR to mathbbR$ which has finite side limits at any real point. Is this function monotonous? I know that the converse is true, but I wonder if this also holds.
real-analysis functions
real-analysis functions
asked Mar 31 at 18:08
MathEnthusiastMathEnthusiast
47913
asked Mar 31 at 18:08
MathEnthusiastMathEnthusiast
47913
asked Mar 31 at 18:08
MathEnthusiastMathEnthusiast
47913
asked Mar 31 at 18:08
MathEnthusiastMathEnthusiast
47913
asked Mar 31 at 18:08
MathEnthusiastMathEnthusiast
47913
47913
2
$begingroup$
Try with $x^2$.
$endgroup$
– Yves Daoust
Mar 31 at 18:16
add a comment |
2
$begingroup$
Try with $x^2$.
$endgroup$
– Yves Daoust
Mar 31 at 18:16
2
2
$begingroup$
Try with $x^2$.
$endgroup$
– Yves Daoust
Mar 31 at 18:16
$begingroup$
Try with $x^2$.
$endgroup$
– Yves Daoust
Mar 31 at 18:16
add a comment |
1 Answer
1
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oldest
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$begingroup$
Consider $sin(x)$ and you'll have your answer :)
answered Mar 31 at 18:14
EurekaEureka
876114
$endgroup$
add a comment |
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$begingroup$
Consider $sin(x)$ and you'll have your answer :)
answered Mar 31 at 18:14
EurekaEureka
876114
$endgroup$
add a comment |
$begingroup$
Consider $sin(x)$ and you'll have your answer :)
answered Mar 31 at 18:14
EurekaEureka
876114
$endgroup$
add a comment |
$begingroup$
Consider $sin(x)$ and you'll have your answer :)
answered Mar 31 at 18:14
EurekaEureka
876114
$endgroup$
Consider $sin(x)$ and you'll have your answer :)
answered Mar 31 at 18:14
EurekaEureka
876114
answered Mar 31 at 18:14
EurekaEureka
876114
answered Mar 31 at 18:14
EurekaEureka
876114
answered Mar 31 at 18:14
EurekaEureka
876114
876114
add a comment |
add a comment |
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$begingroup$
Try with $x^2$.
$endgroup$
– Yves Daoust
Mar 31 at 18:16