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Smallest means exactly what you think it would mean. I don't think there is any ambiguity there.
Well, every periodic function has infinitely many periods.
Hm, but that function would not be periodic.
Well, as it was shown that no function can have uncountable extrema, the Weierstrass function cannot have uncountable extrema.
Fixed post 59:
Speaking of which, here is a question.
Does every non-constant periodic function have a smallest positive period?
It is not periodic, so it does not have a period.
Speaking of which, here is a question.
Does every non-constant periodic function have a smallest positive period?
Well, each of those intervals has rational endpoints, so there are certainly countably many.
It's more likely in Serbian, but that's not important. The book is in English.
Well, I found this: http://books.google.rs/books?id=Cqk5AAA … um&f=false
I asked a professor today about this problem and also found out the answer to your question.
It's needed to be shown that each of those extreme points can be isolated inside an interval so that no two intervals intersect.
I don't think there are uncountably many peaks, but I'm not sure.
Actually, the answer is that it does not exist, but I don't know how to prove that.
It is not. It has countably many such points.
Strict, not strictly.
E.g. point x is a strict local maximum of the function f if there is a neighbourhood of x such that for each point y in that neighbourhood, f(y)<f(x).
2) Is there a function with uncountably many strict extremal points?
Are you sure? You need to multiply both the denominator and the numerator by that.
Myltiply both by
I was referring to the tea kettle principle. It does not apply here.
You can "rationalise" both the denominator and the numerator.
That principle does not apply here.
I am getting 3/2.
L'Hopital is not needed here.
Okay, I'll wait.
Still, the right side cannot contain y, then.
Because the left side does not have x at all. Should the limit operator be on the other side?
Hi;
Is this the question?
Prove:
That does not make sense.
You are slowly morphing into a math type and therefore think that you need lots of set theory.
Math types need topology to function properly.
it seems like the numbers 1, 2 and 3 are going periodically upwards from left to right.