Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

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I don't think 1 is correct. Have you tried to plot it. It's wild.

I don't think it exists.

Where did he not allow the squeeze theorem?

Also, A\B can be used to mean A-B.

Hi MIF

Not sure if that's the general case, but I've seen the bolded "I" be used mostly for irrational numbers.

I heard it was used a long time ago by the primitive native tribes of San Serriffe.

Supremum.

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?

It can, why do you think it can't?

Well, it certainly does exist.

Think of it this way: If you take any number that's a period, there is a number smaller than that one that's also a period.

It is, but can you find such a function?

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:

anonimnystefy wrote:

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.