Math Is Fun Forum
You are not logged in.
- Topics: Active | Unanswered
#76 2014-11-12 05:14:31
Re: Is there such a function?
Infinite descent!
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
Offline
#77 2014-11-12 05:28:42
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: Is there such a function?
Hm?
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
Offline
#78 2014-11-12 05:29:17
Re: Is there such a function?
How can that be non-constant?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
Offline
#79 2014-11-12 06:22:53
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: Is there such a function?
It can, why do you think it can't?
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
Offline
#80 2014-11-12 08:48:25
Re: Is there such a function?
Speaking of which, here is a question.
Does every non-constant periodic function have a smallest positive period?
Let f be the function defined by f(x) = 1 if x is rational and f(x) = 0 if x is irrational.
Then every rational number is a period of f.
Last edited by benice (2014-11-12 08:58:41)
Offline
#81 2014-11-12 11:27:07
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: Is there such a function?
Yep! 
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
Offline
#82 2014-11-12 11:31:32
Re: Is there such a function?
Great!
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
Offline
#83 2014-11-12 12:01:59
- ShivamS
- Member
- Registered: 2011-02-07
- Posts: 3,648
Re: Is there such a function?
Does every non-constant periodic function have a smallest positive period?
Take the Dirichlet function for example.
Offline
#84 2014-11-12 12:26:28
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: Is there such a function?
Yep. Here's another interesting one:
Does continuity of a function f on [a,b] guarantee continuity of the function g(x)=sup{f(t)|a≤t≤x} on [a,b]? What about differentiability?
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
Offline
#85 2014-11-12 12:27:15
Re: Is there such a function?
What is sup?
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
Offline
#86 2014-11-12 12:30:18
- anonimnystefy
- Real Member
- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,049
Re: Is there such a function?
Supremum.
Here lies the reader who will never open this book. He is forever dead.
Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.
Offline
#87 2017-03-26 03:30:13
Re: Is there such a function?
Yep. Here's another interesting one:
Does continuity of a function f on [a,b] guarantee continuity of the function g(x)=sup{f(t)|a≤t≤x} on [a,b]? What about differentiability?
Yes, this is indeed an interesting one. Continuity, I think so. Differentiablity, not sure. I will have to make a more serious attempt
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
Offline
#88 2017-03-26 03:56:17
Re: Is there such a function?
2) Is there a function with uncountably many strict extremal points?
No, there cannot be. The following is a proof, which I found on the internet, is for maximas. We could produce a similar proof for minimas and then union them to get the same result.
I cannot believe that I actually found a solution to this problem that I understood. I thoroughly remember having this conversation here on this forum two years ago, it still feels like yesterday. I remember the sequences of events that followed.
And now, here I am fully (well, at least much better) being able to comprehend this. It does turn out I have learnt something.
'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
I'm not crazy, my mother had me tested.
Offline